Bridget Copley

Hamida Henry Davis

Reconciling Causal and Modal Representations for Two Salish Out of Control Forms

 were the first to make the link between the O

Introduction

St'át'imcets (also known as "Lillooet") and Skwwú7mesh (also known as "Squamish") are Salish languages spoken in present-day southwestern British Columbia, Canada. The St'át'imcets (St') circumfix ka...a and the Skwwú7mesh (Sk) particle txw have both been called "out of control" markers [START_REF] Demirdache | Out of control in St'á'imcets Salish and event (de)composition. Theoretical Issues on the Morphology-Syntax Interface[END_REF][START_REF] Matthewson | Modality in St'át'imcets[END_REF][START_REF] Davis | A unified modal semantics for 'out-of-control' marking in St'at'imcets[END_REF][START_REF] Davis | Out of control marking as circumstantial modality in St'át'imcets[END_REF][START_REF] Jacobs | Txw as an out of control marker[END_REF][START_REF] Jacobs | Control in Skwwú7mesh[END_REF]. They share a number of similar readings, for instance, in (1a,b), a "no choice" or "had to" reading:

(1) a. ka-wat'k'=kán-a OOC-vomit-1SG.SUBJ-OOC i=ts'aqw-ann'-an when.PAST=eat-DIR-1SG.ERG ti=qvl-wííl'c=a DET-bad-become=EXIS ts'úqwaz' fish 'I had to throw up after eating that rotten fish.' St'át'imcets Davis et al. 2007: (61) b. na RL men just

txw OOC

xay-m laugh-INTR ta DET stá7uxwlh children 'The children had to laugh' (even though they were trying not to).' Skwwú7mesh Jacobs 2007: (16) The notion of "control" [START_REF] Thompson | The control system: A major category in the grammar of Salishan languages[END_REF]) refers to morphology, pervasive in Salish languages, that seems to have to do with the amount of control that the agent has over the event.1 Different Salish langauges have different morphological systems for control. Broadly speaking, St' ka…a has "no choice" readings as well as abilitative readings [START_REF] Davis | A unified modal semantics for 'out-of-control' marking in St'at'imcets[END_REF][START_REF] Davis | Out of control marking as circumstantial modality in St'át'imcets[END_REF], while Sk txw contributes only "no choice" meaning, with abilitative readings contributed by "limited control" transitivizers and intransitivizers [START_REF] Jacobs | Txw as an out of control marker[END_REF][START_REF] Jacobs | Control in Skwwú7mesh[END_REF].

Both causal [START_REF] Demirdache | Out of control in St'á'imcets Salish and event (de)composition. Theoretical Issues on the Morphology-Syntax Interface[END_REF][START_REF] Davis | On lexical verb meanings: Evidence from Salish[END_REF][START_REF] Jacobs | Txw as an out of control marker[END_REF]) and modal [START_REF] Matthewson | Modality in St'át'imcets[END_REF][START_REF] Davis | A unified modal semantics for 'out-of-control' marking in St'at'imcets[END_REF][START_REF] Davis | Out of control marking as circumstantial modality in St'át'imcets[END_REF][START_REF] Jacobs | Control in Skwwú7mesh[END_REF] analyses have been given for St' ka…a and Sk txw. Despite much insightful analysis, it is still not clear whether a causal or a modal framework carves this domain of meanings more cleanly at its joints; nor is it clear why St'át'imcets ka...a and Sk txw share some but not all readings.

Here I propose that these forms can be understood in a hybrid framework that places the modal notions among the nodes of a causal model [START_REF] Pearl | Causality: Models, reasoning and inference[END_REF]. In effect, desires (or for inanimate entities, dispositions2) and abilities are represented as states that causally influence eventualities. Thus, as in the causal approaches, we can consider causal relations explicitly; and as in the modal approaches, causal influences can be represented without entailing the actuality of the eventuality. An additional key component of this approach is the notion of efficacy [START_REF] Copley | O'odham cem: when the world isn't inertial[END_REF][START_REF] Copley | A force-theoretic framework for event structure[END_REF]: the idea that one particular influence gets to determine what happens.3 When these formal components are assembled, ka...a and txw end up sharing the meaning that the influence associated with the subject is not efficacious. This strongly echos the causal analyses cited above. The subject's influence itself can be either a desire/disposition, which leads to "no choice" readings, or an ability, which leads to abilitative readings; this is reminiscent of the modal analyses. Using these causal and modal elements, the proposal yields a paradigm of anti-efficacious causal structures to be further investigated.

Here I give the broadest possible overview of readings that ka…a and txw sentences have, without going into their numerous interactions with eventuality type and morphology. For comprehensive exposition and analysis of ka…a, see [START_REF] Demirdache | Out of control in St'á'imcets Salish and event (de)composition. Theoretical Issues on the Morphology-Syntax Interface[END_REF], [START_REF] Davis | Salish evidence on the causative-inchoative alternation[END_REF], [START_REF] Matthewson | Modality in St'át'imcets[END_REF], and [START_REF] Davis | A unified modal semantics for 'out-of-control' marking in St'at'imcets[END_REF][START_REF] Davis | Out of control marking as circumstantial modality in St'át'imcets[END_REF]; and for txw, [START_REF] Jacobs | Txw as an out of control marker[END_REF][START_REF] Jacobs | Control in Skwwú7mesh[END_REF]. I follow [START_REF] Davis | A unified modal semantics for 'out-of-control' marking in St'at'imcets[END_REF][START_REF] Davis | Out of control marking as circumstantial modality in St'át'imcets[END_REF] in highlighting a distinction between "no choice" and what I will call "abilitative" readings; this distinction will be crucial to the proposal.

As we saw above in (1), the "no choice" category are readings where actions are construed as involuntary or uncontrollable. These also include sentences with nuances that include suddenness, unexpectedness, and unwillingness:

(2) a. nilh FOC láti7 there ka-t'ál=s-a OOC-stop=3POSS-OOC ta=káoh-s-a DET=car-3POSS=EXIS 'His car suddenly stopped.' St'át'imcets Davis et al. 2007: (53) ta det sitn basket 'She decided to make a berry basket.' (Context: she didn't want to, but she either decided to because of circumstances, or was made to because she was expected to.) Skwwú7mesh Jacobs 2007: (23) [START_REF] Davis | A unified modal semantics for 'out-of-control' marking in St'at'imcets[END_REF][START_REF] Davis | Out of control marking as circumstantial modality in St'át'imcets[END_REF]) also include accidental readings, as in (4a), in the no choice category. I propose here to instead include them in the abilitative category, based in part on the fact that Sk txw excludes them along with (other) abilitative readings, and in part on a consideration to be discussed below. The manageto and ability readings are also contributed by ooc marking in St', with ability being the most prominent reading for ka…a (H. Davis, p.c.). Note that unaccusatives do not occur with the ability meaning, as shown in (4a), and unergatives do not occur with the accidental meaning, as shown in (4c). In Sk , as mentioned above, abilitative readings are contributed by limited control morphemes rather than ooc txw [START_REF] Jacobs | Txw as an out of control marker[END_REF][START_REF] Jacobs | Control in Skwwú7mesh[END_REF] Both causal and modal analyses have been given for ka…a and txw. On the causal side, [START_REF] Demirdache | Out of control in St'á'imcets Salish and event (de)composition. Theoretical Issues on the Morphology-Syntax Interface[END_REF] and [START_REF] Davis | On lexical verb meanings: Evidence from Salish[END_REF] argue that St' ka…a "supresses either the initial subevent in the event structure of a predicate, or the name … that is associated with this subevent" (Demirdache 1997: 98). Crucial to this analysis is the insight that even unaccusative predicates in St' have a causative lexical representation [START_REF] Davis | Salish evidence on the causative-inchoative alternation[END_REF]. As for Sk txw, a causal analysis is given by [START_REF] Jacobs | Txw as an out of control marker[END_REF], who proposes that txw is a marker of "the causer of the event" [being] "different than the grammatical subject of the sentence"; and tellingly, that "[t]his separates volitionality from causation" Jacobs (2007: 281). These proposals crucially identify a key component of the meanings studied: namely, that the causal influence associated with the subject is removed or set aside in some sense. However, what is lacking is a clear explication of how to represent abilitative flavor in ka…a sentences such as in (4), as well as how volition is to be represented in such a way as to interact with causal relations in sentences such as (3c) above. In addition, as [START_REF] Davis | A unified modal semantics for 'out-of-control' marking in St'at'imcets[END_REF] point out, certain St' examples with ka…a lack actuality entailments for what would be the result. Thus, a causal relation CAUSE such that 𝑒 1 CAUSE 𝑒 2 entails the actuality of 𝑒 2 , as in e.g. [START_REF] Lewis | Causation[END_REF], is a priori excluded.

These considerations, among others, motivated modal approaches to these meanings, as in [START_REF] Matthewson | Modality in St'át'imcets[END_REF] and [START_REF] Davis | A unified modal semantics for 'out-of-control' marking in St'at'imcets[END_REF][START_REF] Davis | Out of control marking as circumstantial modality in St'át'imcets[END_REF] and [START_REF] Jacobs | Control in Skwwú7mesh[END_REF]. [START_REF] Davis | A unified modal semantics for 'out-of-control' marking in St'at'imcets[END_REF][START_REF] Davis | Out of control marking as circumstantial modality in St'át'imcets[END_REF] propose that St' ka…a is a circumstantial modal with variable quantificational force, i.e. either universal or existential force. The idea in a nutshell is that the no choice readings have universal force, and the abilitative readings have existential force. Thus causal information is used (in the choice of modal base and ordering source) but without entailing the result; careful attention is paid to the presence or absence of actuality entailments. Jacobs (2011: 412) follows Davis et al. in suggesting that a modal analysis is plausible for Sk txw. However, in this approach to these ooc forms, as Jacobs comments, there remains more to say about how eventuality types and valence interact with the core modal meaning. Indeed, it is not terribly clear why formally modal meanings would interact so pervasively with eventuality types and valence, as ooc morphology does (though this is a longstanding problem for modal denotations in general, not limited to ooc phenomena). Most seriously, there are well-known problems with treating ability as a circumstantial possibility modal [START_REF] Nadathur | Causality and aspect in ability, actuality, and implicativity[END_REF].

How can these approaches be reconciled in a way that sheds light on the meanings of ka…a and txw? First we must note that it is possible to represent explicit causal relations even when the effect does not occur [START_REF] Copley | Theories of causation should inform linguistic theory and vice versa[END_REF]. In this paper I will do just this, using a novel class of causal models [START_REF] Pearl | Causality: Models, reasoning and inference[END_REF] based on the notion of efficacy [START_REF] Copley | O'odham cem: when the world isn't inertial[END_REF][START_REF] Copley | A force-theoretic framework for event structure[END_REF]. From there, we will follow the existing causal analyses in explicitly representing causal relations. Explicit representation of causation will more closely align with action-based treatments of ability, and should eventually allow for more grounded explanations of the interactions with eventuality types and valence, through general constraints on what kind of event can be caused by which agent (or by no agent at all). Finally, we will follow the existing modal analyses in underlining the importance in the first place of the modal notions, namely desires/dispositions, and abilities.

Formal framework

Causal model basics

For our purposes, a causal model [START_REF] Pearl | Causality: Models, reasoning and inference[END_REF] is a formal representation of the structure that causal relations give to a conceptual model of the world.5 Causal models are formally represented by means of a directed acyclic graph. There is a set of variables that are the vertices (or nodes) of the graph. These variables are allowed to have various values. These are connected by a set of edges (or arrows). The causal model conveys that the values of some variables influence the values of other variables, according to both the arrows of the graph (which show the direction of causation) and the functions associated with one or more of these arrows (which give more information about which values go together). For instance, 𝐴 → 𝐵 represents that the value of 𝐵 is dependent in some way on the value of 𝐴, without specifying which values go together.

Information about which values go together is something that comes from world knowledge. Consider, for instance, a scenario where either lightning or arson may cause a forest fire. We can model this scenario with the causal structure 𝐿 → 𝐹 ← 𝑀, where 𝐿 = 1 iff there is lightning, 𝐹 = 1 iff there is fire, and 𝑀 = 1 iff the match is lit. The possible values of each node are thus the truth values of the associated proposition. The entire structure is a "collider" structure, since two influences in a sense "collide". We can represent the values of F given the values of 𝐿 and 𝑀: so, 𝐹 = 𝐹 𝐹 (𝐿, 𝑀). In this case, 𝐹 𝐹 happens to be the OR function. In principle, we could set 𝐹 𝐹 to be any function we like that takes the values of the other variables and returns the value of 𝑋, but it should faithfully reflect world knowledge.

Causal models are useful for us in that they allow us to represent the directionality of causation (given by the variables and the arrows) without a particular variable necessarily being given a particular value. Specifically, we will be interested in cases of "anti-efficacy", where 𝑋 → 𝑌 is in the model, but 𝑌 does not have the value that 𝑋's influence would have been expected to make it have.

Efficacy models

An influence is efficacious [START_REF] Copley | O'odham cem: when the world isn't inertial[END_REF][START_REF] Copley | A force-theoretic framework for event structure[END_REF], when it alone determines what happens. The idea that this notion should be represented in our model drives the constraints to causal models that I will propose here. I assume that an efficacious influence can be identified.

Let's call a causal model with the following local (i.e., ceteris paribus, defeasible) and global licensing conditions an efficacy model. Local listening says that an arrow from 𝐴 to 𝐵 is only licensed if the value of 𝐵 "listens" to the value of 𝐵 when all other arrows into 𝐵 are erased. We consider two ways to for this to occur: the arrow is associated either with a "stimulatory"/"positive slope" function, where the value of 𝐴 positively correlates with the value of 𝐵, marked with a "+"; or it is associated with an "inhibitory"/"negative slope" function, where the value of 𝐴 negatively correlates with the value of 𝐵, marked with a "-" (and see [START_REF] Lewis | Causation[END_REF][START_REF] Croft | Verbs: Aspect and causal structure[END_REF]). Since we are using truth values as the values, there are only two possible functions that arrows can correspond to, as in ( 5): Zooming out, we assume a limited version of the causal principle, namely that certain events need to have causes (though some can occur spontaneously; see [START_REF] Haspelmath | More on the typology of inchoative/causative verb alternations[END_REF]. And finally, we need to answer the question of what valuations are possible if we have a collider structure. Colliders in an efficacy model are globally indeterminate even though each arrow is locally determinate; for example, in the model 𝑋 → 𝑌 ← 𝑍, both 𝑋 and 𝑍 "propose" a value for 𝑌 . The "winning" influence is simply the one that we pick out as winning. That is, when 𝑋 → 𝑌 is part of the model: then 𝑋 is (globally) efficacious for 𝑌 iff for all nodes 𝑍 in the model: the value of 𝐹 𝑌 (𝑋, 𝑍)-that is to say, the value of 𝑌 in this model-is set to the value of 𝑓 𝑋𝑌 (𝑋).

Modal notions in a causal model

We will need to model both desires/dispositions and abilities of the subject. (I will write simply "desire" from here on out, with the understanding that dispositions are included.) I propose here that desire and ability be seen, for our current purposes, purely as states that influence eventualities. In this way they can be represented in the causal model as nodes that influence other nodes. The backstory of what these notions really are can certainly still be modeled using quantification over sets of possible worlds, but we will not do so here. These modal states will be represented by "subject-related influence" variables that can have the value 0 or 1. We will also need, of course, a node for whether the eventuality occurs or not (eliding the telic/atelic distinction); call it 𝐸.

We can identify two kinds of subject-related influence nodes. Desire nodes ("𝐷") represent a desire that an eventuality of the kind described by the verb occurs; so, a desire for 𝐸 = 1. The way desires are understood here is as dispositional properties of the subject: in the absence of other, interfering influences, they influence the event to occur. Ability nodes ("𝐴") represent properties that require certain conditions, and if such conditions are present, and if interfering influences are absent, 𝐸 = 1.

Let's note that the subject can be in a state that is neither desiring for the eventuality to happen nor desiring for the eventuality not to happen; likewise, the subject can be in a state where they neither have the ability to make the eventuality happen, nor the ability to ensure that the eventuality does not happen. In other words, each of the desire domain and the ability domain allow not two, but three possible states that the subject can be in (represented below in Figure 1). We will also find it useful to represent two additional kinds of nodes: D, for "dislike", and à for the ability to avoid the eventuality's happening, which I will term "avoid-ability" (= the ability to avoid). These nodes carve up the space of subject's states as follows: The desire and dislike nodes will be the influencing nodes for the "no-choice" readings, while the ability and avoid-ability nodes are the influencing nodes for the abilitative readings. This makes sense, because if we think about the two kinds of nodes, they recapitulate the universal (necessity) and existential (possibility) modal analyses [START_REF] Davis | A unified modal semantics for 'out-of-control' marking in St'at'imcets[END_REF][START_REF] Davis | Out of control marking as circumstantial modality in St'át'imcets[END_REF], but in a causal system. With the desire/dislike nodes, the eventuality happens if nothing inteferes; while with the ability/avoid-ability nodes, even if nothing interferes, the eventuality only happens sometimes, in the presence of certain other conditions.

⏟⏟⏟ D = 1 ∶ dislike for 𝐸 = 1 ⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟ D = 0 ∶ no dislike for 𝐸 = 1 𝐷 = 0 ∶ no desire for 𝐸 = 1 ⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞ 𝐷 = 1 ∶ desire for 𝐸 = 1 ⏞⏞⏞ ⏟⏟⏟ Ã =
Using D and à is especially interesting for the unwillingly and accidentally readings. In the case of the unwillingly readings (e.g. (3c) above), speakers describe the subject as not wanting the event to occur, i.e., having a desire that it not occur. But wanting and not wanting, in this sense, do not pick out complementary sets of states, because there is a middle option of indifference. Thus, unwillingness should not be represented as the negation of wanting; instead we give it its own kind of variable. As for accidentally readings: In principle, such a reading could be a case of unwillingness ( D = 1). But if it is, why is the accidental reading sensitive to, e.g., whether a predicate is unaccusative (felicitous, as in (4a)) or unergative (infelicitous, as in (4c))? It's perfectly possible to have desires about unergative events. On the other hand, if these readings are really about avoid-ability, there is a plausible reason for this pattern; events satisfying unergative predicates are comparatively easier to avoid ( à = 1) and events satisfying unaccusative predicates are more spontaneous, so perhaps sometimes unavoidable ( à = 0, and see [START_REF] Haspelmath | More on the typology of inchoative/causative verb alternations[END_REF]. This is why I propose to represent accidentally readings as cases where à = 0.

Finally, as a reminder, inanimate subjects can also occur with ooc marking. Particular attention has been paid to these in St' especially (e.g. [START_REF] Demirdache | Out of control in St'á'imcets Salish and event (de)composition. Theoretical Issues on the Morphology-Syntax Interface[END_REF][START_REF] Davis | A unified modal semantics for 'out-of-control' marking in St'at'imcets[END_REF][START_REF] Davis | Out of control marking as circumstantial modality in St'át'imcets[END_REF] where unaccusatives (as in (2)) and ability readings (as in ( 6)) need not have animate subjects.

(6) u, oh kéla7=t'u7 first=ADD ka-kwís-a OOC-rain-OOC lts7a here 'Oh, it can really rain here.' St'át'imcets Davis et al. 2007: (51a) So how are inanimate subjects to be treated in this analysis if we are talking about "desire" and "dislike"? The idea already mentioned above is that "desire" should be understood as something like a disposition toward a kind of eventuality occurring. Additionally, the subject-related influencing nodes can, as far as the grammar is concerned, generally occur with inanimate subjects. However, grammar is not the only consideration here. Combinations of certain influencing properties with certain subjects and certain kinds of eventualities are expected to be impossible because of world knowledge as to which entities can influence which eventualities and how they do so. So, for instance, perhaps it is not possible for inanimate entities to have the ability to avoid the occurrence of an eventuality. All this could be investigated in conjunction with a deeper dive into the compositional semantics of ooc marked-sentences.

Proposal

My proposal is that ooc marking in St' and Sk both have an anti-efficacy meaning. In other words, the original influencing node and arrow provided by the sentence does not get to determine what happens. Anti-efficacy, taken together with the assumption that certain events need causes, invokes the existence of a second influence on 𝐸 that is efficacious for 𝐸, making a collider structure. St' by ka…a contributes desire, dislike, ability, and avoid-ability readings, while Sk txw contributes desire and dislike readings only.

While there is not space here to do justice to the compositionality of the aspectual-verbal systems in St' or Sk , nor to make precise the differences between at-issue and not-at-issue meaning, we can at least sketch out the beginnings of an analysis by showing how anti-efficacy works, and by presenting the space of possible anti-efficacy readings. In the efficacy model diagrams that follow, the node, value, arrow, and function of the second, entailed influence are marked with parentheses. The exclamation point marks the value of 𝐸, because it is surprising given the value of the original influencing node and the original arrow's function. The checkmark (✓) marks the function (the arrow) that is efficacious and therefore gets to determine the value of 𝐸; the × marks the arrow that is not efficacious. The function corresponding to each arrow, either 𝑓 + or 𝑓 -as defined in (5) above, is notated above the arrow.

So, for instance, we can identify unexpectedly readings (such as in (3b) above) as those where the subject lacks a certain desire that would, in the absence of other influences, lead to the eventuality occurring; but despite this lack, the eventuality turns out to occur anyway. This state of affairs is shown in (7a). We can follow [START_REF] Davis | A unified modal semantics for 'out-of-control' marking in St'at'imcets[END_REF][START_REF] Davis | Out of control marking as circumstantial modality in St'át'imcets[END_REF] in linking the unexpectedly reading to the suddenly reading: If the causal route from desire to the 𝐸-eventuality usually takes time, and if the causal route from the additional entailed influence 𝑋 does not, the onset of the 𝐸-eventuality might well be comparatively sudden.

In (7b), the influencing node is a dislike, so normally, in the absence of interfering influences, the eventuality would not be expected to occur. Yet nonetheless the eventuality occurs, despite the subject's unwillingness. There does seem to be a difference here between attested examples in St' and those attested in Sk ; both permit "uncontrollable" eventualities (as in (2a) above), but only Sk seems to permit "controllable" eventualities (as in (3c) above). This apparent contrast should be further investigated in light of the present proposal.

(7) a. Unexpectedly reading b. Unwillingly reading

𝐷 𝑓 + --→ × 𝐸 ( 𝑓 + ← -- ✓ 𝑋) 0 1! (1) D 𝑓 - --→ × 𝐸 ( 𝑓 + ← -- ✓ 𝑋) 1 1! (1)
We turn now to the abilitative readings of St' ka…a. Where the influencing node is an ability and 𝐸 = 1, we expect manage-to readings, as in (4b) above, where the subject lacks a property (or lacks the totality of the properties) that would ensure that 𝐸 gets the value 1; but lo and behold, 𝐸 = 1 anyway, and we therefore must accommodate the second influence 𝑋. And as we have seen, accidental readings, such as in (4a) above, can be represented with an avoid-ability influencing node. What this conveys is that the subject would normally, in the absence of other influences, have the ability to avoid the occurrence of the eventuality, but because of the anti-efficacy contributed by ka…a, the eventuality in fact occurs.

𝐴 𝑓 + --→ × 𝐸 ( 𝑓 + ← -- ✓ 𝑋) 0 1! (1) Ã 𝑓 + --→ × 𝐸 ( 𝑓 + ← -- ✓ 𝑋) 1 1! (1)
Note, however, that although the examples above all have 𝐸 = 1, this does not strictly speaking seem to be a requirement for ka…a [START_REF] Davis | A unified modal semantics for 'out-of-control' marking in St'at'imcets[END_REF][START_REF] Davis | Out of control marking as circumstantial modality in St'át'imcets[END_REF], including for no choice readings. As Davis et al. point out, cancellations of no choice readings are difficult to elicit. I accept their reasoning that things that circumstantially must happen usually do happen; when they do not, in the current framework it's because the model being used was not faithful to reality.

The ability cases, however, do not have this difficult quality. I propose that ability readings of ka…a are cases where the influencing node is an ability 𝐴, and 𝐴 = 1, and since 𝐴 is not efficacious, 𝐸 = 0. This idea awaits confirmation, but it finds support in the observation [START_REF] Matthewson | Modality in St'át'imcets[END_REF] Context: Not only are the climate and soil right, but you have reason to believe that it's actually possible there is some sagebrush.

The possibility that 𝐸 = 0 opens up a range of other, in principle possible, anti-efficacious meanings, which are detailed in the second row of the table in Figure 2. The "actuality" readings from ( 7) and ( 8) are in the first row of the table. Throughout, the entailed second influence 𝑋 is not represented. The labels on the cells correspond to readings, but there may be more readings that might correspond to any one cell. The gray cells are those readings where I do not know the status of the judgments in St'. [START_REF] Matthewson | Modality in St'át'imcets[END_REF] implies a connection between ka…a and frustrative meanings.6 I suspect that the "declined offer" and "near miss" cells might be ruled out on the grounds that both nodes have a zero value, which would not satisfy even the weakest (disjunctive) condition that the verb might impose on those values.

Interestingly, however, Sk limited control marking, when it gets an ability reading, apparently does not entail the non-occurrence of the eventuality, as shown in ( 10 Context: An adult is playing peek-a-boo with a child. This point should be further explored, but it may suggest that the cell marked "ability" in Figure 2 is not appropriate for Sk limited control. Instead perhaps an efficacious ability analysis, where 𝐴 = 1 and 𝐸 = 1, could be considered as a possible analysis for Sk limited control ability readings.

Conclusion

I hope to have demonstrated the usefulness of a certain class of causal models which I termed "efficacy models", in conjunction with modal notions such as desire and ability, for understanding out of control forms in these languages. The resulting representations suggest that both ka…a in St'át'imcets and txw in Skwwú7mesh may share an "anti-efficacy" meaning, and may differ in whether their meanings can have an abilitative influencing node. This proposal also provides a paradigm of anti-efficacious meanings for further investigation.

  Local determinacy says that each arrow 𝑋 → 𝑌 in the model is associated with a function 𝑓 𝑋𝑌 which is one of the two functions given in (5); and local (or defeasible) efficacy says that if all other arrows into 𝑌 are erased, 𝑌 = 𝑓 𝑋𝑌 (𝑋). That is, the value of 𝑌 is set to what 𝑋 says it is.

Figure 1 :

 1 Figure 1: Desire, dislike, ability, and avoid-ability

SubjectFigure 2 :

 2 Figure 2: The space of possible anti-efficacy readings on this proposal

-sek-s-às-a OOC-hit-CAUS-ERG-OOC

		.4
	(4)	a. kati	sq'úm'ts-a	ti	twéw'w'et-a.	St'át'imcets
		DET	ball-DET	DET	boy-DET	Demirdache 1997: (10e)
		'The boy hit the ball (accidentally).'/*The boy is able to hit the ball.'
		b. ka

-gwél-s=kan-a OOC-burn-CAUS=1SG.SUBJ-OOC

	St'át'imcets
	Davis et al. 2007: (6a)
	'I managed to get it lit.'
	c. ka

-álkst-kan-a OOC-work-1SG.SUB-OOC

	St'át'imcets
	Demirdache 1997: (8a)
	'I am able to work.'/*'I accidentally worked.'

  that in St', the evidential k'a, instead of ooc ka…a, is generally used when it's possible that 𝐸 = 1:

	(9)	a. wa7		ka-ríp-a		ku	káwkew	kents7á	St'át'imcets
		IMPERF	OOC-grow-OOC	DET	sagebrush	DEICTIC	Matthewson et al. 2005: (16a)
		'Sagebrush can grow around here.'
		(Okay if speaker knows no sagebrush actually grows here.)
		Consultant's comment: "If somebody brought some seeds it would grow here-it's just a
		possibility it would grow here."
		b. wa7	k'a		kents7á	sxek		ku	káwkew	St'át'imcets
		be	EVID	DEICTIC	maybe	DET	sagebrush	Matthewson et al. 2005: note 7
		'Sagebrush might be growing around here.'

[START_REF] Jacobs | Txw as an out of control marker[END_REF] reports, however, that limited control is sometimes compatible with txw.

For a gentle introduction to causal models, see Chapter 1 of[START_REF] Pearl | The book of why: The new science of cause and effect[END_REF].

Matthewson et al.'s (2005) discussion of the morpheme ka in St' is also relevant here; ka on its own seems to enforce the non-actuality of the eventuality.


Ludwig Dumetz
email: ludwig.dumetz.1@ulaval.ca

Jonathan Gaudreault
email: jonathan.gaudreault@ift.ulaval.ca

Hind Bril

El Haouzi
email: elhaouzi5@univ-lorraine.fr

André Thomas
email: andre.thomas@univ-lorraine.fr

Nadia Lehoux
email: nadia.lehoux@gmc.ulaval.ca

Philippe Marier
email: philippe.marier@forac.ulaval.ca

Bril El-Haouzi

Tactical-operational coordination of a divergent production systems with coproduction

Keywords: Tactical-operational coordination, Lumber production planning, Simulation, Forest industry, Divergent process, Coproduction Tactical-operational coordination, Lumber production planning, Simulation, Forest industry, Divergent process, Coproduction

Various optimization tools have been used in industry to facilitate production planning at different levels of aggregation. Choosing the interoperability mechanisms of these systems, such as the planning frequencies, the information passed between them and the interpretation that other systems must make of them, has always been a challenge. This work focusses on production planning at the tactical and operational levels in North American sawmills, a commodity industry characterized by volatile prices and a divergent production process with coproduction. In this context, tactical planning produces aggregated plans, and information from these plans can be used as targets and / or constraints at the operational level (e.g. quantities to be produced / kept in stock per product and per period, sales targets, etc.). A simulation of this production system was therefore developed, encompassing the planning process and the market dynamic, to compare and evaluate the impact of different coordination approaches on business economic performance. Results showed that the type of information which should be shared from the tactical level to the operational level varies according to several factors, including the company's order acceptance policy, prices seasonality, and the presence or absence of overcapacity on the market.

INTRODUCTION

Production planning at the tactical and operational levels is a widely studied topic. The forest industry is not an exception and many optimization models exist to plan lumber production in order to meet demand [START_REF] D'amours | Chaînes de création de valeur[END_REF]. The forest industry operates in a particular context defined inter alia by a divergent flow of products (several finished products from the same raw material) with coproduction (production of several products at the same time).

The tactical planning of a sawmill aims to obtain an aggregated plan for a horizon of 12 months, which will generally be updated once a month. It integrates the three main activities of the production process which are the sawing, drying and finishing operations. This planning takes into account the company's strategic objectives, available resources, available capacity, long-term commitments, forecasts of demand and supply constraints. The tactical plan aims to maximize the expected income; it predicts how resources will be used and acts as a guide for sales and production work. In fact, information from tactical planning is used to determine the operational plan (which has a much shorter horizon of a few weeks) in order to ensure income over a long period as well as a good operational performance. For example, the tactical level might recommend keeping stocks of a particular product during certain periods in order to be able to take advantage of an improvement in future prices, which the operational level alone cannot anticipate.

Since tactical models do not have the same level of accuracy as operational models, it is necessary to communicate and / or disaggregate information from the tactical level in order to transfer it to the operational level. This information can take the form of, for example, production targets (what to produce at each period for each operation included in the timber production process), inventory targets (what quantity to keep in stock at the end of a given period) or information about estimated monthly sales prices.

This study contributes to scientific literature by addressing the coordination issue between two planning levels which have different time horizons. It proposes an approach to design the production planning process incorporating both tactical and operational planning levels. Various information can be extracted from the tactical plan to become constraints and / or targets that will be used at the operational level.

However, the type of information which should be transferred from the tactical level to the operational level depends on various factors, such as the order acceptance policy used at the sales level (Availableto-promise [ATP], Capable-to-promise [CTP]), the importance of price seasonality, or the presence of overcapacity on the market. The evaluation of the different scenarios is carried out using simulation. The simulation platform of [START_REF] Dumetz | Evaluating order acceptance policies for divergent production systems with coproduction[END_REF] is used to simulate the production system, the planning process at the tactical and operational levels, as well as the market behavior, using a rolling horizon. This simulation also implements a tactical planning model and three operational planning models (one for each production activity: sawing, drying and finishing operations) from Marier et al. (2014a[START_REF] Marier | Implementing a MIP model to plane and schedule wood finishing operation in a sawmill: lessons learned[END_REF][START_REF] Marier | Kiln Drying Operations Scheduling with Dynamic Composition of Loading Patterns[END_REF]. The company's performance (i.e. sales volumes, revenues, inventories) is evaluated according to the planning system in place, the order acceptance policy used (ATP, CTP), and the context of the market (volume of demand, seasonality of prices). Results show that certain information / targets / constraints shared from the tactical level to the operational level can lead to performance improvement or degradation depending on the context. This is crucial information for industries as it has a direct impact on the performance of the company, in terms of generated income.

The article is organized as follows. Section 2 presents a brief literature review on hierarchical planning as well as on the peculiarities of tactical and operational planning in the North American lumber industry.

Section 3 introduces the simulation model used to complete the experiments and Section 4 describes the experiments and the results obtained. Finally, Section 5 concludes the paper.

Preliminary concepts

Hierarchical planning

The planning process encompasses a large number of decisions at different hierarchical levels [START_REF] Vollmann | Manufacturing planning and control for supply chain management[END_REF]. At the strategic level, long-term decisions are made (business plan). At the tactical level, mid-term decisions, covering an average planning horizon of 6 to 18 months, involve defining the quantities to produce and to stock so as to meet the objectives defined at the strategic level and achieve the financial objectives defined in the budget. The operational level establishes a detailed plan. The horizon is very short, about a few weeks, usually reviewed weekly or more often depending on the business context.

There are many mathematical models for tactical and operational production planning in various industries (see for example Díaz-Madroñero et al., 2014). Nevertheless, it remains essential to ensure synergy between the two levels of planning. For example, all of the orders anticipated by the tactical level will not necessarily occur and the operational planning must take that fact into account.

It is difficult to design and validate a planning process that incorporates both tactical and operational levels while maintaining good consistency. The time scales used for planning (both the size of the planning horizon and the review frequency) at these two levels are not the same, which implies some form of disaggregation. Typically, monthly data is used for tactical planning while the operational level needs daily data. In addition, the tactical level sometimes works with product families1 while the operational level works with individual products. The tactical level's "macro-vision" is sometimes necessary for several reasons: on the one hand, there is not enough knowledge of the data and only aggregated data is available or makes sense, and on the other hand, the problem has to be simplified to be solved in its entirety [START_REF] Simchi-Levi | Designing and managing the supply chain: concepts, strategies, and case studies[END_REF].

For many years, much work has led to proposals for obtaining tactical plans and / or disaggregation of these tactical plans into production plans for the operational level. The term Hierarchical Production Planning (HPP) (see [START_REF] Bitran | On the design of hierarchical production planning systems[END_REF] is often used to describe the general planning process in stages. A problem that is too complex to solve may be simplified and solved in an aggregated way and the result may be used to solve the more detailed problem (Hax and Meal, 1984). [START_REF] Mckay | A review of hierarchical production planning and its applicability for modern manufacturing[END_REF] provided a review of the concept of HPP and highlighted different applications in the manufacturing sector. [START_REF] Aghezzaf | A robust hierarchical production planning for a capacitated two-stage production system[END_REF] used this approach to solve a planning problem in a two-level environment, composed of semi-finished products (aggregate level) and finished products (disaggregated level), by proposing a robust HPP model. Based on [START_REF] Genin | Planification tactique robuste avec usage d'un APS[END_REF] work on the stability and robustness of tactical plans and Ortiz and [START_REF] Ortiz Araya | Proposition of disaggregation method for tactical robust planning[END_REF] work on the disaggregation of tactical plans into master production schedules through several optimization models, Thomas et al. (2012) proposed a methodology to disaggregate a tactical plan. They showed, among other things, that this disaggregation allowed stability of the operational plan under certain conditions (building stocks). The tactical plan provides aggregated information, i.e. product family per month. A first model makes it possible to transform these quantities of product families by month into a number of finished products per month. A heuristic is then used to provide a stable operational plan (finished products per week). Ortiz and Albornoz (2012) developed a methodology based on the concept of HPP allowing a disaggregation of a monthly plan of product families into a weekly plan of finished products. The case studied concerned a company that produces reusable bags in Chile and Peru. The disaggregation is done using several optimization models imposing constraints to keep the coherence of the final production plan. Vogel et al. (2016) compared two approaches: hierarchical production planning versus integrated production planning. They assumed that (1) some of the reasons justifying the use of a hierarchical approach to plan production at different levels are not legitimate and (2) optimizing a series of subproblems can lead to sub-optimality of the general problem. They proposed two models, a hierarchical model taking into account an aggregate level and a disaggregated level, and an integrated model combining these different levels. In their context, they showed that the integrated approach delivers a better result and that the necessary computation time, although longer than for the hierarchical model, is acceptable. Even though this study is interesting, most of the practical cases require a hierarchical decomposition as well as the use of several specialized models at the operational level (e.g. several factories). In the case of sawmills, it is currently not possible to use a single model to plan sawing, drying and finishing operations (see [START_REF] Gaudreault | Distributed operations planning in the lumber supply chain: models and coordination[END_REF]).

Production planning for the North-America lumber industry

This study focuses on operations planning at the tactical and operational levels in North American sawmills. Lumber production consists of three sub-processes in almost independent facilities: sawing (turning logs into planks), drying (removing excess moisture from the wood), and finishing (to give parts the desired finish, then grading and trimming parts). Each operation is different and has its own constraints and characteristics (for more information, see [START_REF] Gaudreault | Distributed operations planning in the lumber supply chain: models and coordination[END_REF]. Production planning is a real challenge because of the particular characteristics of this industry. Indeed, from the same raw material, several finished products are obtained (divergent process) simultaneously (coproduction) (see Öner and Bilgiç, 2008). The impact of this divergent flow is very significant and affects the intermediate products at the sawing, drying and finishing operations, which multiplies the number of finished products originating from the same log. In addition, the market price for these products are highly susceptible to seasonality [START_REF] Marier | Gestion intégrée des ventes et des opérations dans l'industrie du sciage[END_REF]. The North American lumber market is a convenience market whose products must meet the National Lumber Grades Authority (NLGA) 2 criteria. The price therefore 2 The North American lumber system relies on a standardization process lead by the National Lumber Grades Authority (NLGA) that defines strict dimensions and qualities. This makes lumber a fluctuates greatly depending on supply and demand.

In this context, planning at the tactical level aims to define objectives for the production of sawing, drying and finishing, by product and by period, taking into account that the coproduction phenomenon limits the options of the company (since producing one product entails the production of several, maybe unnecessary, coproducts). The tactical models used are therefore developed to take these constraints into account. They also make it possible to establish inventory targets (i.e. for which products to build stocks) and when these quantities should be sold to take advantage of the market prices. Again, storage constraints and costs need to be taken into account as well as contract constraints. Depending on the volume of demand and the price fluctuation, the strategy to be used may vary widely (Marier et al., 2014a). There are many planning models at the tactical level, including [START_REF] Singer | Internal supply chain management in the Chilean sawmill industry[END_REF] who proposed an optimization model for production planning in a Chilean sawmill, or [START_REF] Marier | Gestion intégrée des ventes et des opérations dans l'industrie du sciage[END_REF] and [START_REF] Marier | S&OP network model for commodity lumber products[END_REF] who introduced a tactical MIP model integrating operations (sawing, drying and finishing) planning and sales.

Planning at the operational level defines the exact operations schedule by taking into account the actual demand and the information provided by the tactical level. The tactical level serves as a reference frame, allowing the operational level to carry out its short-term planning while taking into account future visions. Different models to plan for each of the three lumber production operations are also needed at this decision level. For the sawing operation, planning models generally include the selection of cutting patterns which generate either a better volume of sawn timber or a better material yield or aim to promote the cutting of a particular product. The cutting pattern represents how the log should be cut and which products will be obtained. There are a multitude of cutting patterns, taking into account the natural characteristics of the log. [START_REF] Maturana | Scheduling production for a sawmill: A comparison of a mathematical model versus a heuristic[END_REF] listed some operational planning models such as the ones developed by [START_REF] Occeña | Grasp -A prototype interactive graphic sawing program[END_REF], [START_REF] Todoroki | Combined primary and secondary log breakdown optimization[END_REF] and [START_REF] Winn | Alog: A spreadsheet-based program for generating artificial logs[END_REF].

They also developed a deterministic planning model for sawing operations for a sawmill in Chile. commodity market. The situation is different in Europe where most products are made to order according to specific characteristics.

However, in their model, they assume that all data are known. [START_REF] Varas | Scheduling production for a sawmill: A robust optimization approach[END_REF] improved this model by taking into account uncertainty in demand and raw material, using a robust optimization approach.

For the drying operation, several models exist such as those of [START_REF] Yaghubian | Dry-or-buy decision support for dry kiln scheduling in furniture production[END_REF] who developed a planning model that takes into account the possibility of buying dry wood or drying it and [START_REF] Marier | Kiln Drying Operations Scheduling with Dynamic Composition of Loading Patterns[END_REF] who proposed a MIP model that dynamically generates loading patterns. A loading pattern indicates how a dryer should be filled, taking into account the different wood species (which do not dry at the same speed), wood dimensions and the characteristics of the dryer. For the finishing operation, [START_REF] Gaudreault | Distributed operations planning in the lumber supply chain: models and coordination[END_REF] and [START_REF] Marier | S&OP network model for commodity lumber products[END_REF] proposed planning models that maximize the value produced by taking demand into account and minimizing delays.

In forestry literature, tactical disaggregation and tactical / operational coordination approaches are also studied. As it is the case for other industries, the main challenges are to obtain a certain level of coherence between the decisions taken at the different levels.

In forestry operations, [START_REF] Beaudoin | Hierarchical forest management with anticipation: an application to tacticaloperational planning integration[END_REF] showed how to take into account the impact of decisions made at the tactical level on the feasibility of the operational plan. The authors propose an application of the [START_REF] Schneeweiss | Distributed decision making-a unified approach[END_REF] generic hierarchical model allowing for a better alignment between the different levels of planning. Their application is for the wood harvesting capacity, which determines the number of contractors to be hired during the year. For the sawing industry in Chile, [START_REF] Alvarez | Improving consistency of tactical and operational planning using robust optimization[END_REF] used robust optimization to obtain tactical plans, generating robust solutions that ensure good operational feasibility. Recently, Lobos and Verra (2016) studied the problem of tactical and operational planning in a sawmill in Chile. Their study focuses on the use of aggregated and disaggregated models at the tactical level and their short-and long-term impact on storage costs, raw material purchase costs and production costs. In their context, a model is said to be disaggregated if it uses several flow patterns for sawing and a model is said aggregated if it uses an average of all these flow patterns. They used a "two-stage formulation" [START_REF] Birge | Introduction to stochastic programming[END_REF] to coordinate long-term decisions and short-term decisions and presented four models covering these two levels of planning (tactical and operational). In their study, only sawing is taken into account while in North America, sawmills also need to dry and finish their wood in order to meet NLGA standards, which complicates the coordination between tactical and operational levels.

Simulation framework

This study uses proven planning models ensuring feasible production plans to evaluate the impact of different types of information shared from the tactical level to the operational level performance of a typical North American sawmill.

In order to compare and evaluate the impact of different coordination approaches between the tactical level and the operational level on business economic performance, both the decentralized planning process and production process (sawing, drying and finishing) are simulated. The simulation incorporates the physical production system, the planning process implemented, the market context as well as the company's order acceptance policy, whether it is ATP or CTP.

The production planning process incorporates tactical and operational planning levels. The information is shared from the tactical level to the operational level as constraints or targets to be respected (e.g. quantities to be produced / kept in stock per product and per period, sales targets, sales price forecasts, etc.).

Configurating the framework

The simulation framework proposed by [START_REF] Dumetz | Evaluating order acceptance policies for divergent production systems with coproduction[END_REF][START_REF] Dumetz | Simulation and Evaluation of Coordination Mechanisms for a Decentralized Lumber Production System with Coproduction[END_REF] was exploited and a tactical decision level was added (see Figure 1). The simulation framework was developed in the Simio environment, a discrete event simulation software. Orders are generated following a Poisson distribution as proposed by Ben [START_REF] Ali | A Multi-Level Framework for Demand Fulfillment in a Make-to-Stock Environment -A Case Study in Canadian Softwood Lumber Industry[END_REF].

These orders are then accepted or rejected based on an order acceptance policy (e.g. ATP or CTP). In particular, with the ATP policy (APICS, 2012), an order of size Q is accepted only if Q is smaller or equal to the expected stocks for each period of the planning horizon after the due date.

Q ≤ I + ∑ (P t -E t ) D-1 t=now -max D≤t≤T {∑ (E k -P k ) t k=D } (1)
where D is the due date of the order, T is the simulation horizon, I is the current inventory, Pt is the production at period t and Et are the commitments at period t. The CTP policy (APICS, 2012) amounts to first attempting to accept an order with the ATP policy, as previously explained. If the order cannot be accepted using the ATP policy, a provisional production plan is drawn up, including this new order, to check if the order can be satisfied without compromising previous commitments. If the order cannot be made in time, the customer is notified, and it is assumed that he has withdrawn his request. When an order is accepted, the simulation model waits for the delivery date and the quantity available and the order is delivered.

Demand

The simulation framework incorporates a custom-built Enterprise Resource Planning (ERP) that is responsible for tactical and operational planning. This ERP was programmed in C # .net environment, which makes use of different specialized models and algorithms taken from the literature. At the tactical level, the Sales and Operations Planning model for the lumber industry published by Marier et al. (2014a) is used. This integrated model provides a production plan for sawing, drying and finishing over a oneyear horizon. The constraints at different stages of production (raw material, dryer configuration, flow patterns, ...) are taken into account. Based on the assumed sales prices from forecasts, a production plan is generated with the aim of maximizing income and reducing costs. Figure 2 shows the inputs and outputs used in this model. At the operational level, three independent planning models for the sawing, drying and finishing operations are also exploited. For sawing, a model from [START_REF] Marier | Implementing a MIP model to plane and schedule wood finishing operation in a sawmill: lessons learned[END_REF] based on the work of [START_REF] Gaudreault | Distributed operations planning in the lumber supply chain: models and coordination[END_REF] is used. This model maximizes produced value while generating a sawing plan which takes into consideration the raw material (the available logs), the sawing capacity, and the different cutting patterns. In particular, the output plan states which process is used, when, for how long as well as how many sawn products are produced. We suppose that the raw material is not limiting the production and that production is available 14 hours per day, 7 days a week. All cutting patterns have the same and replanning occurs once a week. Figure 3 shows the inputs and outputs used by this model. 2016) is used. A kiln dryer can be represented as a huge container (defined by its length, height and width) where bundles to be dried are assembled on a wagon and then pushed inside the kiln. The planning horizon is 4 weeks with replanning occurring once a week. The model can be used to minimize order lateness or to maximize production value. The output drying plan states which wood bundle to dry, when, in which dryer, as well as how to load the kiln (loading pattern)

Figure 4 shows the inputs and outputs used in this model. For more information about the MIP model, see [START_REF] Marier | Kiln Drying Operations Scheduling with Dynamic Composition of Loading Patterns[END_REF].

Operational level coordination

As the operational models work in a decentralized manner, a mechanism is therefore required to ensure coordination. This coordination mechanism makes sure that the need or the demand for each subsequent operation will be taken into account. It is based on a hybrid push / pull approach which considers the decoupling point in the production system. The decoupling point is located between the drying unit and the finishing unit (Figure 6), as finishing is the bottleneck of the system. A decoupling point is defined by APICS (2008) as "the locations in the product structure or distribution network where inventory is placed to create independence between processes or entities". et al. (2014a) showed that this does not help tactical models, which are linear models whose resolution time is little affected by the number of products.

Validation of the framework

In simulation studies, validation ensures the veracity of the result and analysis [START_REF] Sargent | Validation and Verification of Simulation Models[END_REF]. As the system we modeled does not really exist, the simulation could not be validated by comparing historical production data with our simulation model outputs. However, the mathematical models exploited have been validated in the past and are already being used by a Canadian forest products company. In addition, the simulation framework used is the same as the one developed and tested by [START_REF] Dumetz | Evaluating order acceptance policies for divergent production systems with coproduction[END_REF] to evaluate the impact of different order acceptance policies (ATP, CTP, Stock). In the present study, the framework was modified, and some features integrated so as to take into account the tactical level. The model was validated by using the same set of data and parameters as in [START_REF] Dumetz | Evaluating order acceptance policies for divergent production systems with coproduction[END_REF].

Experiments

To compare and evaluate the impact of different coordination approaches between the tactical level and the operational level on business economic performance, different planning approaches were devised.

Each approach is defined by (1) an order acceptance policy (ATP or CTP), as well as by ( 2) the type of information transmitted from the tactical level to the operational level. In [START_REF] Dumetz | Evaluating order acceptance policies for divergent production systems with coproduction[END_REF] and [START_REF] Dumetz | Simulation and Evaluation of Coordination Mechanisms for a Decentralized Lumber Production System with Coproduction[END_REF], order acceptance policies have been studied for industries facing divergent processes with coproduction. ATP and CTP were the order acceptance policies that showed the best performances in terms of accepted orders and lower average inventory. Those policies are furthermore enough flexible to be adapted to the forest products industry context. These two order acceptance policies were therefore chosen for the present experimentations. The type of information transmitted from the tactical to the operational level (2) could simply be a forecast of the product market price for the next month or more specific production and inventory targets. As the experiments took 350 hours of calculation, we had to target the key aspects to evaluate so as to limit the number of experiments to conduct. The information we selected is typically the one used in the North American sawing industry while being available from the tactical plan. -Order acceptance does not create a future shortage.

(Red dashed line)

-Order acceptance is made under the ATP policy, with additional constraints (inventory targets must be met).

-Order acceptance does not create a future shortage.

CTP (Full blue line)

-Order is established if it can be accepted under the ATP policy.

-If this is not the case, the production plan is modified to include this new order only if it does not compromise previous commitments (Full red line)

-Order is established if it can be accepted under the ATP policy, subject to the additional constraints (inventory targets must be met).

-If this is not the case, the production plan is modified to include this new order only if it does not compromise previous commitments under constraints that the new production plan meets the production and inventory targets.

Order acceptance policy

Tactical instructions

Working with industrial partners, parameters of the tactical model and the operational models were defined to be representative of a typical Canadian sawmill, although only the 10 most representative products were kept. For example, cutting patterns, drying processes and finishing recipes were set according to real patterns, adapted to fit these 10 products. To determine this, we used a real production plan of a partner company. This production plan listed all the products produced over a year. We used the Pareto law and found that 80% of the production volume concerned only 10 products. Those products were therefore the ones used in the experimentation as taking into account the remaining 20% would only have weighed down the model. The sale prices associated with these products were real prices provided by the sawmill (we were provided with historic data). In our study, the operational costs are those linked to each processing stage (sawing, drying, and finishing). We assume that they are the same for each cutting pattern, each finishing recipe, and each drying process. The simulation covers a twoyear production horizon. The raw material supply (logs) has infinite capacity. The demand for each product is randomly generated using a Poisson distribution as in Ben [START_REF] Ali | A Multi-Level Framework for Demand Fulfillment in a Make-to-Stock Environment -A Case Study in Canadian Softwood Lumber Industry[END_REF]. The delivery time required by the customer is randomly generated using a triangular distribution. Each order consists of a single product with a fixed order quantity of 50 MPMP. The PMP board foot is a measurement used for lumber in North America and a MPMP corresponds to one thousand feet of board. In addition, two other parameters define the market context: (1) the magnitude of the seasonality of product prices and (2) the annual demand intensity in relation to production capacity. With respect to price seasonality (1), the industrial data used for this case study reflected the seasonality of prices on the market. In addition to the original demand scenario (average seasonality), two other seasonality scenarios were defined for analysis purposes: one where there was no seasonality (a product has the same average value each month)

and one where the seasonality was amplified (strong seasonality). To amplify the seasonality of a product's sales price, the 6 highest selling prices of the year were increased by $ 50 (or 10% on average), whereas the other 6 sales prices (lowest prices) were decreased by $ 50. Figure 8 illustrates the seasonality amplification process for a product. It represents the number of orders received by the company in 1 year. For example, a company that receives a significant demand for 1 year will sell almost everything it produces. Conversely, if demand is low, a company will have to choose carefully what will be produced (finished products) in order to sell it to the right customer. In this case, it is important to produce the right product at the right time. In these experimentations the demand intensity represents the entire range between these two extremes. To quantify it, the intensity of demand is expressed as a percentage of the company's maximum production capacity. At a 100% intensity, the demand that the company will receive over one year will be equal to its entire annual production capacity. Other percentages are also tested since it has been shown (see [START_REF] Dumetz | Evaluating order acceptance policies for divergent production systems with coproduction[END_REF] that due to the coproduction phenomenon, the demand must be much greater than the production capacity to be able to sell all the products. For this reason, this intensity was varied between 200% and 3000%. This quantity is distributed among the different products manufactured and represents the typical demand profile of a North American sawmill, although the number of products taken into account has been aggregated. The following table shows the quantity of demand that a company may receive every year for an intensity of 100% and 300%. Quantity is expressed in thousand board feet (MFBM).. For an intensity of 300%, the company will receive a quantity of demand equivalent to 3 times its maximal production capacity over the year. The demand is distributed throughout the year randomly. As 1 order represents 50 MPMP, it is possible to receive several orders for the same product in the same week depending on the intensity.

A total of 15 replications per scenario were conducted in order to obtain significant confidence intervals (95% confidence level). The total simulation time was 350 hours.

In these experimentations, stochastic events affecting the production process were not taken into account.

Hence, all the production planned at the operational level was produced. With this assumption, results between scenarios could be compared to determine the impact of the choice of the information inherited from the tactical level on the generated revenue.

Results

Market without seasonality

Figure 9 shows the income according to the demand intensity in a market without seasonality.

Demand intensity

Figure 9: Income according to demand intensity, type of targets transmitted from the tactical level to the operational level and order acceptance policy used (no seasonality).

Considering results concerning the ATP policy (dashed lines), providing production targets (red dashed line) at the operational level gives a better income than only providing operational price information (blue dashed line). The phenomenon is especially noticeable at low intensity. This is because if the operational level works only on the basis of the selling price (blue dashed line), it will produce a basket of products with a maximal value, without taking into account the possible volume to be ordered in the future. The demand for some products will then be too low and it will not be possible to sell all of the created stock. Many orders that are not in line with the products stocked will be rejected, and a high level of stock will be observed. On the other hand, when the tactical level transmits production targets and inventory targets (red dashed curve) established by the tactical level, the planning takes into account demand profiles, therefore, the performance is better. Logically, as the demand intensifies, the difference between these two lines decreases.

When strictly comparing the two approaches using the CTP order acceptance policy (full lines), the performance is very similar whether the tactical level provides inventory and production targets (full red line) or simple forecasts of sales price (full blue line). Nevertheless, at low intensity of demand, there is a slight statistically significant added value with the approach that meets the production targets of the tactical level (full red line). Indeed, although the inventory targets are zero because there is no seasonality (so no interest in building a stock in order to sell it when the price is high), this approach is slightly better In general, it can be noted that for low demand intensity (less than 300%), the two approaches using a CTP policy (full lines) perform better than approaches using the ATP policy (dashed curves). In fact, any order accepted in ATP is also accepted in CTP (see the algorithm associated with the CTP policy, section 3.1) and changing the production plan makes it possible to accept more orders (CTP policy). At high intensity (more than 500%), all the curves generate an almost equal income. On the one hand, the demand is large enough that order acceptance using the ATP policy has used up all of the production capacity. On the other hand, the production plans are almost the same, regardless of the tactical targets used. Indeed, the production forecasts from the tactical level are large enough to manufacture only the most profitable products, so production plan will match the one based on sales prices.

Low seasonality market (base case)

Figure 10 shows the income according to the demand intensity for a market with low seasonality. the case without seasonality (previous section), this superiority is valid even at high demand intensity.

Indeed, this comes from the fact that by respecting inventory targets, it is possible to sell a product at a higher price in a future period.

Concerning the approaches using the CTP policy (full red and full blue lines), at low demand intensity (here below 260%), the CTP policy where the tactical level provided simple price forecasts (full blue line) presents a better income. This indicates that when the demand is low with a seasonal market, it is better for operational planning to be based on sales price forecasts rather than following production and inventory targets dictated by the tactical plan. This seems counter-intuitive but is mainly due to the following. Producing a new plan that satisfies the new order, past commitments and inventory targets all together seems very difficult. Many orders are thus refused because the new plan cannot meet all of these constraints. On the other hand, removing the constraint of following the inventory levels allows the CTP policy to be more agile in a situation where demand is low. At high intensity (above 260%), the full red and blue lines are reversed. This indicates that operational planning is better based on production and inventory targets than on price forecasts. This is due to the combination of two elements. As a reminder, any order accepted in ATP is also accepted in CTP (see the algorithm associated with the CTP policy, section 3.1). With this in mind, these two elements are: (1) the approach using the CTP policy based only on the information of the selling prices of the products (full blue line) has a performance resembling that of the associated ATP policy (blue dashed line). Indeed, the approach using the ATP policy is more and more efficient because the demand intensity increases. This leaves fewer possibilities to include a new order using the CTP policy. On the other hand, (2) the generated income using an ATP approach that meets production and inventory targets (red dashed line) is much better when demand intensity increases.

Although it is still difficult to achieve a plan following all constraints, it is still possible to accept some additional orders using the CTP policy. Therefore, this approach using a CTP policy while respecting inventory and production targets (full red line) benefits from the good performance offered by an ATP policy that follows production and inventory targets, which is better than a policy using ATP and information on the selling prices of products.

Finally, in general, when comparing approaches using the same shared information by the tactical level (blue lines for price forecast and red lines for production and inventory targets), approaches using a CTP policy give a better income compared to approaches using an ATP policy. This is valid up to a high demand intensity where income becomes almost equal. In fact, the demand is high enough that all the orders which could be accepted according to the production capacity have already been using the ATP policy: then, using the ATP policy or the CTP policy leads to the same results in terms of income.

High seasonality market

Figure 11 represents the income according to the demand intensity in a situation of high seasonality.

In general, with high seasonality market, the behavior of each line corresponds to what was already observed when the seasonality was lower. The results show that income increases for all cases, compared to Figure 9 where seasonality was low (base case). The seasonality being stronger, the income is also higher, and the crossing point of these same lines does not occur at the same demand intensity (shift to the left).

It is therefore important to take into account these market parameters when choosing tactical targets to be transmitted to the operational level.

Discussion

The sawmilling industry is a process industry where most costs are fixed. The main exceptions are the inventory cost and the procurement cost. In our previous paper [START_REF] Dumetz | Simulation and Evaluation of Coordination Mechanisms for a Decentralized Lumber Production System with Coproduction[END_REF]), we showed that using planning models to maximize sales decreases average stock levels. As for procurement cost, it is directly proportional to production volume thus looking at production value or volume considers them indirectly. That's why sawmill and studies measure throughput. Furthermore, the sawmilling industry in North America typically plans its activities based on a push mode and measures its financial performance regarding the volume produced. Even though a natural resource playing a key role in the ecosystem is processed, it is rare to see a sawmill using a performance indicator not related to the revenues generated or the volume produced.

These results demonstrate the importance of coordinating production planning at the tactical and operational decision levels in order to achieve a plan that meets the long-term goals as well as the orders that arrive daily. This coordination is especially important because of the particular context studied here (a divergent process with coproduction). The information transmitted from the tactical level to the operational level which was selected for this study (information on sales prices, production target and inventory target) are targets commonly used in the forest products industry. Results showed that the type of information transmitted, and the market context directly impacted the revenues generated. Highly relevant information for the industry, companies in the forestry sector could use these findings as a decision-making tool which recommends the best choice of information to transmit from the tactical level to the operational level according to their business context (production parameters, planning approach and market context). Moreover, as mentioned, transmitted information is already used in this industry. By remaining faithful to what industrials are doing and avoiding the use of information that these companies would not be able to obtain, the gap between reality and research is limited.

Conclusion

This research studied a production planning process that incorporated tactical and operational decisionmaking levels of North American sawmills. Production plans based on various information transmitted from the tactical level to the operational level were compared and evaluated by simulating the production system, the planning process as well as market behavior. In this context, the information shared from the tactical level to the operational level became targets or constraints (e.g. quantities to be produced / kept in stock per product and per period, information on the sales prices of the products used at the tactical level). These targets or constraints were used by the operational level to plan production at each stage of the lumber production process and thus meet demand. Results showed that in certain market contexts (defined by a volume of demand and a seasonality in the prices of products), the choice of the targets shared by the tactical plan and seen as constraints for the operational plan could lead to a degradation of the company's performances because of the impossibility of respecting these constraints. Conversely, for other market contexts, these same targets helped to better manage inventories and demand, especially by selling at the right time (when the selling price is higher) thus leading to an increase in income. For example, at a high demand intensity, meeting inventory targets would create a stock to sell later, at a higher price. Conversely, following these same inventory targets at a low demand intensity would lead to poor performance in terms of generated income. This is because the demand is too low or poorly known; stocks cannot be sold. These findings are vital for industries as they demonstrate the importance of coordination between various production planning levels and which information should be transmitted from the tactical plan to the operational plan to maximize income, depending on their business context.

These results were obtained in a particular context, with specific market parameters and business data.

These results are therefore not prescriptive but are intended to show the importance and difficulty of choosing the coordination approach for a divergent production system with coproduction, and therefore the need for a systematic analysis of using the methodology proposed in this article. Furthermore, the wood industry is not the only one presenting characteristics such as coproduction and divergent processes. This study could be very interesting for other industries facing divergent processes (several products obtained from the same raw material) with coproduction (the products are obtained at the same).

This methodology could very well be adapted for example to the food industry, the oil industry, or the "float glass" industry.

In future work, it would be interesting to vary the calculation of targets in the tactical model based on information other than prices. For example, by setting limits by product type, setting maximum inventory levels instead of minimum levels to keep, or by proposing limits for inventories (e.g. product A must maintain its inventory between the values x and y where y> x). This last proposal could possibly offer good solutions since the inventory targets are currently hard constraints to respect. If these targets were bounds, this would probably offer better opportunities to accept orders and thus increase the generated income. Finally, stochastic events can also be added to the production process. Due to failure, for example, what was previously planned could not be produced and late orders could occur. Firstly, the framework would then be much closer to reality since a company would inevitably face production issues. Secondly, robustness of the framework could also be studied.

(Red dashed line)

-Order acceptance is made under the ATP policy, with additional constraints (inventory targets must be met).

-Order acceptance does not create a future shortage.

CTP (Full blue line)

-Order is established if it can be accepted under the ATP policy.

-If this is not the case, the production plan is modified to include this new order only if it does not compromise previous commitments

(Full red line)

-Order is established if it can be accepted under the ATP policy, subject to the additional constraints (inventory targets must be met).

-If this is not the case, the production plan is modified to include this new order only if it does not compromise previous commitments under constraints that the new production plan meets the production and inventory targets.

Order acceptance policy

Tactical instructions

Demand intensity

Tables

Figure 1 :

 1 Figure 1: Conceptual representation of the simulation framework (adapted from Dumetz et al., 2016 and 2018)

Figure 2 :

 2 Figure2: Inputs and outputs used in the model fromMarier et al. (2014a)

Figure 3 :

 3 Figure3: Inputs and outputs used by the model from[START_REF] Marier | Implementing a MIP model to plane and schedule wood finishing operation in a sawmill: lessons learned[END_REF]

Figure 4 :•

 4 Figure4: Inputs and outputs used in the model from[START_REF] Marier | Kiln Drying Operations Scheduling with Dynamic Composition of Loading Patterns[END_REF]

Figure 5 :

 5 Figure5: Inputs and outputs used in the model from[START_REF] Marier | Implementing a MIP model to plane and schedule wood finishing operation in a sawmill: lessons learned[END_REF]

Figure 6 :

 6 Figure 6: Decoupling point before the finishing stage (From Dumetz et al. (2018))

Figure 7 :

 7 Figure 7: Tactical-operational coordination

Figure 8 :

 8 Figure 8: Seasonal amplification process

  targets + CTP because it allows taking into account the demand profile.

Figure 10 :

 10 Figure 10: Income according to demand intensity, type of targets transmitted from tactical level to operational level and order acceptance policy (low seasonality)

Figure 11 :

 11 Figure 11: Income according to demand intensity, type of targets transmitted from the tactical level to the operational level and order acceptance policy (high seasonality)

Figure 1 :Figure 2 :Figure 3 :

 123 Figure 1: Conceptual representation of the simulation framework (adapted from[START_REF] Dumetz | Evaluating order acceptance policies for divergent production systems with coproduction[END_REF][START_REF] Dumetz | Simulation and Evaluation of Coordination Mechanisms for a Decentralized Lumber Production System with Coproduction[END_REF]

  Responsible for the production planning over a period of 12 months for sawing, drying and finishing operations by taking into account supply and operational constraints, available raw material, past commitments

							Tactical level
	Production planning	module	Sawing		Operational level Drying	Finishing
							Production plan		Inventory
	Simulation of the process of	generating, accepting and	shipping orders	Orders generation	Order	Accept/refuse according to various policies Refused order	Accepted order	Shipping Waiting for due date and available quantity

Table 2 :

 2 Quantity of demand received in one year in MFBM (intensity of 100% and 300%)

		650
		600
		550
	Pices $	350 450 500 400					Regular prices Extended seasonality
		300
		250
		J	F M A M J	J	A	S	O N D
			Months

Table 1 :

 1 Description of the planning approaches evaluated

Table 2 :

 2 Quantity of demand received in one year in MFBM (intensity of 100% and 300%)

		100% of the	300% of the
		maximal	maximal
		production	production
	Product	capacity (MBFM)	capacity (MBFM)
	P1	3 145	9 435
	P2	10 464	31 392
	P3	14 517	43 551
	P4	22 064	66 192
	P5	50 362	151 086
	P6	265	795
	P7	1 258	3 774
	P8	3 586	10 758
	P9	18	54
	P10	13	39

In our experiments, the products were not aggregated into families, in accordance with current practice of North American sawmills. The forecasts for these distinct convenience products are generally available by product. Furthermore, aggregation into families did not greatly reduce the planning model's complexity.

Acknowledgements

We would like to thank the research consortium FORAC and its partners, as well as the financial support from NSERC.

Accepted order

Order Simulation of the process of generating, accepting and shipping orders

Production planning module

Tactical level Responsible for the production planning over a period of 12 months for sawing, drying and finishing operations by taking into account supply and operational constraints, available raw material, past commitments

Operational level

Inventory Production plan

Drying

Finishing Sawing S&OP from Marier et al. (2014a) • Available log