Strategic Information Sharing in a Dynamic Supply Chain with a Carrier under Complex Uncertainty

Whether to use an information sharing mechanism is investigated in a dynamic supply chain, where onemanufacturer, one carrier, and one retailer are faced with uncertain yield, demand, and lead time during multiple periods. Each member is modeled as an adaptive agent based on multiagent technique, and their decisions can be adjusted timely to adapt to external environment. There are two choices for the whole supply chain to deal with uncertain risks: information sharing (IS) or no information sharing (NS). Under strategy IS, the information aboutmarket demand and the retailer’s inventory can be sharedwithin the supply chain. For each strategy, the effects of yield, demand, and lead time uncertainties on costs of the supply chain and channel members are studied. It is found that (i) it is rewarding for the upstream manufacturer to use a retailer’s shared information under uncertain yield or demand; (ii) however, information sharing (IS) strategy sometimes should be abandoned for other members and the whole supply chain; (iii) counterintuitively, the increase of transportation time uncertainty benefits the retailer.


Introduction
Information sharing is regarded as a prevalent business strategy to improve operations performance of the supply chain, which has been successfully used in many industries. It is widely acknowledged that information sharing can simultaneously benefit the whole supply chain and each member [1]. A classic case is Nestle and Tesco [2]. By means of sharing sales data between partners, Tesco sharply simplifies the organization procedures and Nestle also reduces the inventory cost. Traditional information sharing focuses on the relationship between sellers and buyers. But with the deepening of labor division, more and more intermediate carriers emerge and are authorized to delivery materials instead of upstream shipper firms. The carrier, a transport service provider, plays a significant role across the supply chain [3]. For instance, Fedex (a third party logistics in America) collaborates with computer manufacturers (such as Apple, Dell, and IBM) and retailers in Taiwan. Some real-time information is shared among them, so that the profit of each member is raised [4]. However, it is not always the case for all firms. As an example of Yingte (a pharmaceutical company in China), it ever failed to decrease cost by sharing information with a carrier and partners. Consequently, strategic information sharing should be used in the actual situation. Strategic information sharing, a flexible strategy, is defined as two choices: information sharing or not. Namely, it is not always necessary to utilize information sharing strategy; sometimes sharing information should be adopted in the supply chain, but it should not be selected at other times. Thus, motivated by these practical observations, it is one of our goals to understand whether information in a multilevel supply chain with a carrier should be shared.
Information sharing decision is usually directly affected by external complex uncertainty [5]. Uncertain market demand and stock information are shared by many companies to mitigate the bullwhip effect, for instance, P&G, Wal-Mart, and Cisco [6]. To cater for time-sensitive consumers, L&TT in Hong Kong presents own production data to upstream suppliers to eliminate the impact of uncertain leadtime risk [7]. Nevertheless, there are also some companies 2 Discrete Dynamics in Nature and Society not willing to provide information to others due to environmental uncertainties. After all, they are afraid that the simple information sharing behavior may not cope with the complex uncertainties [5]. Given the different attitudes toward the information sharing under an uncertain situation, this paper explores how multiple external uncertainties influence information sharing strategy for a supply chain, such as uncertain demand, supply, and lead time.
The actual supply chain is proved to be a dynamic system [8]. The complex dynamics are mainly reflected in two aspects. On the one hand, the supply chain exists in an extremely uncertain environment, where almost all external elements vary all the time. On the other hand, the members in the supply chain are autonomous individuals. Sometimes they adjust own decisions to adapt the dynamic exterior circumstance. We refer to this supply chain as a dynamic supply chain. To the best of our knowledge, the static optimal decision is mainly concentrated on in conventional supply chain studies, which are difficult to reflect the dynamic characteristic of the supply chain. Hence, unlike most researches, the supply chain dynamics in a changing market that consists of multiple periods, however, is the focus of this paper.
An information sharing strategy is investigated in a threelevel supply chain, where one manufacturer, one carrier, and one retailer are faced with uncertain demand, yield and lead time. There are two choices for the supply chain to manage external uncertainties: information sharing (denoted by IS) or not (denoted by NS). Based on the method of multiagent modelling, we compare the total cost of the supply chain and each member in two cases, to address the following issues. (1) Can the information sharing be beneficial to the whole supply chain and each member in a dynamic environment, simultaneously? (2) What are the impacts of some uncertain risk factors on the information sharing decisions? We obtain meaningful management implications. For instance, it is rewarding for the upstream manufacturer to use the retailer's shared information under uncertain yield or demand, whereas information sharing strategy may be abandoned for the whole supply chain and other channel members, and the retailer can obtain more benefits with the increase of transportation time uncertainty.

Literature Review
This paper is related to the information sharing in the supply chain and multiagent modeling.
From the perspective of participants in the supply chain, the information sharing literature can be classified into two streams. The partnership between sellers and buyers is widely discussed in the first stream. For example, Cachon and Fisher [9], Lee et al. [6], and Teunter et al. [10] studied the value of information sharing between upstream and downstream firms. It is concluded that sharing information is beneficial to both parties only under certain conditions. Dejonckheere et al. [11], Chatfield et al. [12], Ma and Ma [13], and Zhao et al. [14] analyzed the impacts of many factors on the well-known bullwhip effect. Aviv [15], Fildes and Kingsman [16], Trapero et al. [17], and Sanders and Wan [18] focused on how forecast errors affect the information sharing, whereas, our paper is different from these researches in that a carrier is regarded as a key supply chain member here. Particularly, we consider the impact of a carrier on the information sharing in a multilevel supply chain. The second stream is about the collaboration with the third party logistics. The typical studies are few. For instance, Wen [19] explored how to forecast shipment of the carrier based on shared information. However, our work places emphasis on identifying complex uncertain factors influencing the information sharing strategy. Tyan et al. [4] and Wen [3] qualitatively described the framework and competitive advantage of collaborative transportation management (CTM). To be different, quantitative study on information sharing behavior for a supply chain with a carrier is conducted in our paper. Chan and Zhang [20] and Li and Chan [21] investigated the benefits of CTM in the mode of make-to-order (MTO), which is somewhat similar to ours. It is found that CTM lowers the total cost and risk for the whole supply chain. Yet the cost of each member is not discussed. As a matter of fact, it is necessary to guarantee each member's benefit in the case of information sharing. In contrast with [20,21], our differences are mainly displayed in four aspects: (1) not only total cost of the whole supply chain, but also that of each individual is examined as well; (2) the manufacturer, exogenous in their researches, is served as an adaptive agent here, which is more in line with practical cases; (3) the supply chain here is a make-to-stock (MTS) production system rather than the MTO system; namely, the manufacturer's order is based on forecast; (4) the effects of multiple uncertain risks are taken into account.
Multiagent modeling is also correlated with our work. The traditional approaches about operations optimization are widely adopted in the supply chain management, which attempts seeking the optimal decision. Instead, this static optimal behavior is usually not in line with practical cases. After all, the supply chain is a complex adaptive system, where each member has to be confronted with an uncertain situation. In addition, practical members across the supply chain are bounded rational [22], who are hard to acquire complete information and find the best decision due to the own ability. In most cases, adaptive learning through past experience is the common method to make decisions. Multiagent modeling (MAM) is a powerful and popular tool to solve the complex dynamic problem owing to the distinct strengths [23]. Consequently, MAM is introduced to depict the dynamic and autonomous features that we primarily focus on. There have been representative literatures on MAM. For example, Swaminathan [23], Long [24], and Yu and Wong [25] construct a framework to explore the supply chain network dynamics. Dogan and Guner [26] and He et al. [27] discuss pricing and ordering policies under demand uncertainty. In addition, some other problems, such as inventory strategies [28], products management [29], and scheduling [30,31] are examined by many scholars as well.
To sum up, this paper contributes to the literature in several aspects. First, unlike many literatures, the carrier is considered as a crucial member in a supply chain. The issue of whether to share information with an intermediary carrier in a supply chain is investigated. Each party's cost especially is studied in detail. Second, we further explore the motivation to share information under external uncertainties. To be specific, the impacts of uncertain demand, yield, and lead time on information sharing are discussed. Lastly, the complex supply chain's dynamic and adaptive natures are captured in this paper. In particular, each member is capable of altering own decisions in a dynamic environment.

The Overall Structure and Problem Description.
Consider a supply chain with one manufacturer, one retailer, and one carrier in the presence of complex uncertainties. It is assumed that demand, , follows a normal distribution; i.e., ∼ ( 1 , 2 1 ). And the upstream manufacturer's yield is unstable. There are two methods (strategies) for the whole supply chain to cope with uncertain risks: information sharing (IS) or not (NS). Under strategy IS, real-time information on market demand and the retailer's inventory is shared among all members. Therefore, the valuable information can be used by each member to adjust own decision to adapt to the external environment. However, demand and inventory information is not shared under strategy NS, where it is difficult to make dynamic decisions for some members. The detailed channel structures under two strategies are showed in Figure 1. The whole event of our model is dynamic, which includes two stages.
Stage 1. The whole supply chain jointly decides whether to share information among all members: IS or NS. Stage 2. Under the given strategy, the second stage is made up of multiple periods. During each period, the sequence of events is as follows: (1) At the beginning of each period, the manufacturer forecasts an order in advance and completes production. (2) The demand is realized.
(3) The retailer firstly meets the back orders and market demand through available inventory in hand. Then, the order point is adjusted through sharing information under strategy IS; but it is constant under strategy NS. Lastly, whether to place an order upstream is decided. Unmet demand will be delayed to next period if the inventory is enough. (4) The transportation capability is forecasted in advance by the carrier with shared information under strategy IS; but it is constant under strategy NS. (5) If the manufacturer accepts the retailer's order, the order is transported to the retailer by the carrier (when yield is not enough, insufficient orders are delayed until the next period); otherwise, go to (6). (6) Inventories of the manufacturer and the retailer are checked, and the leftovers will be still sold in next periods. (7) All members compute the total cost to prepare for the next period.
The parameters and variables used throughout the paper are defined in Table 1.   (1) Inventory Check. Before demand is realized in each period, the order quantity from upstream is ensured by the retailer.

The Retailer
is the retailer's order received from upstream in period ; Then, the initial inventory and in-transit inventory are, respectively, updated.
where is the retailer's initial inventory at the beginning of period ; −1 is the ending inventory in the last period t-1; is the total in-transit inventory in period .
(2) Demand Fulfillment. The former back orders and market demand are met through available inventory.
where is the remaining inventory in period ; , −1 is the retailer's total delayed order in the last period t-1.
(3) Inventory Management. It is assumed that famous ( , ) inventory policy is used. Similar to Axsater [32], where is the order point; 0 is the initial value of , and it is a constant under strategy IS, ( = 1, 2, ....) = 0 ; is the maximum inventory level, and the initial inventory in the first period 1 = ; is the safety factor on inventory; is the retailer's unit delayed cost; ℎ is the unit inventory holding cost; is the retailer's ordering cost; and are, respectively, the lead time of the order process time and transportation time, which are random variables following normal distribution, The current inventory level is The order quantity in this period is In-transit inventory is updated: The back order is checked: (4) Cost. Retailer's total cost is where ( ) , is the retailer's total cost under strategy NS (IS) in period t; the first term is the total inventory holding cost; the second term is the total delayed cost due to unmet demand; the third term is the total carrier's punishment cost; the fourth term is the total manufacturer's punishment cost; and the last term is the fixed order cost.  (1) Forecast and Production. Because of a long lead time for many products, forecast and production must be finished before the selling season in order to respond to consumers rapidly. Hence, the mode of make-to-stock is adopted by the manufacturer.

Retailer's Behavior under
In most cases, the manufacturer cannot know the market demand information clearly under strategy NS. After all, there is a retailer between the manufacturer and consumers market. Further, it is often hard and costly to obtain complete information on uncertain market for a manufacturer. Thus, production quantity is forecasted based on orders from the downstream retailer [6,10].
Similar to Teunter et al. [10], the common moving average method is utilized to forecast the order quantity after N periods. The forecast is based on historical order quantities ( = − 1, − 2, ..., 1) from the retailer. is the forecast value in period . is a constant when < .
Then, the production is competed. It is assumed that the manufacturer is subjected to yield risk due to the uncertain production process. The actual yield is . The common proportion model is used here to describe this random phenomenon. , a multiplication factor, is set to be a random variable following normal distribution, ∼ (1, 2 2 ) [33].

6
Discrete Dynamics in Nature and Society (2) Demand Fulfillment. First, initial inventory is updated in accord with yield and the ending inventory in last period.
− is the manufacturer's initial inventory in period ; − −1 is the ending inventory in the last period t-1.
Then, the demand is met.
is the actual fulfillment quantity in period t; −1 is the manufacturer's total short order in the last period t-1.
(3) Inventory Management. The ending inventory and back order are checked.
are regarded as remaining inventories to be sold in next periods, and short orders , are delayed to fulfill in next periods.
where ( ) , is the manufacturer's total cost under strategy IS (NS) in period ; is unit inventory holding cost; is the manufacturer's unit short cost. Hence, the first term is the total inventory holding cost; the second term is the total short cost; the last term is the fixed order cost.

Manufacturer's Behavior under Strategy IS. Under strategy IS, two behaviors are different from those under strategy NS.
Firstly, the order forecast is dependent on shared market demand data rather than the historical order quantities after periods. Likewise, is a constant as < .
Market demand information can be shared by the retailer under strategy IS, when the manufacturer's production can be forecasted in light of direct market demand rather than a retailer's orders. As a result of the famous bullwhip effect [11], market demand information is more accurate for a manufacturer compared with the information on a retailer' orders.
Secondly, the retailer's inventory is specially managed by the manufacturer. ( , ) policy is still adopted under strategy IS. Due to the shared information of market demand and inventory, on the one hand, the retailer's order process time is removed; i.e., = 0. Thus, the initial value of the order point 0 = 1 ⋅ 3 + ⋅ 3 ⋅ 1 . On the other hand, the order point can be adjusted dynamically after N periods to decrease operations cost; = 0 if < . The decision rule is as below, which is dependent on historical experience [21].
The manufacturer's behavior under two cases is shown in Figure 3.

The Carrier
Agent. The manufacturer's products are transported by the carrier. The delivery lead time is , which is assumed to follow the normal distribution, ∼ ( 3 , 2 3 ). The transportation capacity, , is reserved before each delivery, which is a constant 0 under strategy NS. The cost of maintaining the transportation capacity is = (0 < < 1); is the maintaining cost of unit capacity. If the freight volume is less than , the delivery time is ; otherwise, the delivery time is + 1 [4], and the delayed punishment cost is However, the capacity is a dynamic decision variable under strategy IS. can be determined dynamically in light of some shared information after periods [21].
After each delivery, the total cost of the carrier is computed.
( )  second term is capacity maintaining cost; the third term is the delivery cost. The carrier's behavior under two cases is presented in Figure 4.
Finally, the supply chain's total cost is examined, which is the cost sum of three members.
where ( ) , is the supply chain's total cost under strategy NS (IS) in period t.
Step 3. The manufacturer determines an order based on forecast.
Step 4. Market demand is randomly realized.
Step 5. The retailer firstly fulfills the former back orders and market demand. Then, the order point is updated according to formulas (20) and (21) under strategy IS; however, = 0 under strategy NS. Lastly, the retailer computes the order quantity .
Step 6. The transportation capability is adjusted according to formula (23) under strategy IS; otherwise, = 0 under strategy NS.
Step 7. The products are transported to the retailer by the carrier.
Step 8. The total costs are computed.
Step 9. Enter next period ( ← + 1) and go to Step 3 until termination.
Step 10. Compare the average cost of each member and the whole supply chain under cases IS and NS.

Simulation Experiments and Analysis
In this section, the simulation experiments are firstly designed. Then the effects of uncertain risks on the costs of supply chain members and information sharing strategy are studied.
Parameters of the experiments are set as Table 2. Simulation experiments are conducted on the Eclipse platform   with Java codes. Experiments are carried out considering all parameters with multiple values. This combination method is used in the literature [34,35]. The results in following figures are shown on average. Each simulation is run 100 times with different random seeds, and each time lasts for 500 periods to give each agent abundant time to learn historical experiences.

The Impacts of Uncertain Risks on the Channel Members
Observation 1. Under uncertain yield or demand, strategy IS is a preferable choice for the manufacturer; however, it is not always beneficial for other members to adopt IS.
Firstly, the effects of uncertain yield and demand on the manufacturer's costs under two strategies are explained in Figures 5 and 6 (demand) uncertainty increases. The manufacturer's forecast in each period is derived from the retailer's past orders under strategy NS. As a result of the bullwhip effect, a crucial factor for cost, the manufacturer's forecast is larger than actual demand of the retailer. However, the retailer's stock is managed by the manufacturer under strategy IS, where the order process time is deleted and manufacturer's forecast is based on market demand rather than retailer's orders. Therefore, the bullwhip effect is mitigated, and inventory holding cost and short cost are cut down. Naturally, it is beneficial for the manufacturer to use the retailer's shared information. However, it is not the case for the retailer and the carrier. Then, the impacts of uncertain yield and demand on the retailer's costs are studied. Observed from Figures 7 and 8, strategy IS is profitable for the retailer only when the yield or demand uncertainty is not large. But the cost gap is small when yield or demand uncertainty is large. Taking advantage of sharing information, inventory forecast accuracy can be guaranteed if yield or demand uncertainty is not great. Thus, the retailer's inventory holding cost and delayed short cost decrease. Yet forecast result is affected seriously if uncertainty value is more than a threshold ( 1 > 2 > ). It is difficult to control these unnecessary costs incurred by risks. Thus, unlike the manufacturer, strategy IS is not always superior to the other for the retailer. The value of IS is not obvious as demand or yield uncertainty is large; namely, information sharing should not be applied under the circumstance.
The impacts of yield, demand, and transportation time uncertainties on the carrier's costs are studied as well. Similar to Figures 7 and 8, forecast accuracy is considered as a significant element to trade off whether to share information. Hence, sometimes strategy IS is not better than NS for the carrier. If the uncertainties are large, information sharing is not sensible. Because of the similarity, these details are omitted.
Observation 2. A higher transportation time uncertainty reduces the total cost of the retailer. Figure 9 illustrates how the uncertainty of transportation time affects the retailer's costs. Counterintuitively, the retailer's total cost lowers with the transportation time uncertainty. The uncertain transportation time is regarded as a significant cause for the retailer's stockout crisis. Market demand fill rate decreases because of the increasing uncertainty, which further gives rise to the more delayed short cost for the retailer. However, the penalty cost of the carrier due to delayed delivery is enhanced as well while transportation time becomes more uncertain. Hence, the retailer's total cost finally decreases instead, in that the carrier's penalty cost the retailer obtains offsets increasing short cost.

The Impacts of Uncertain Risks on the Supply Chain
Observation 3. Information sharing is not always beneficial to the whole supply chain under uncertain yield (demand). Strategy IS should be given up when yield (demand) uncertainty is large.
The impact of yield uncertainty on the supply chain costs under two cases are presented in Figure 10. When yield uncertainty is not large, the value of strategy IS is evident; otherwise, strategy IS is worse than NS. Channel members use shared information to adjust decisions and adapt to environment dynamically under strategy IS, which saves unnecessary costs caused by unstable yield if these uncertainties are not large. However, it is not easy to control the risk when uncertainty is large, in that forecast accuracy and quality is cut down. Naturally, the value of information sharing is gradually weakening with the increase of yield uncertainty. The result is similar to that of the demand uncertainty. Therefore, strategy IS should only be adopted by the supply chain when external yield (demand) uncertainty is not large. Otherwise, information sharing behavior should be avoided.
Observation 4. The cost caused by order process uncertainty can be mitigated obviously under strategy IS; but the advantage of strategy IS is not evident in terms of transportation time uncertainty.
The relationship between ordering process uncertainty and supply chain costs is showed in Figure 11. The cost under strategy IS is smaller than that under NS. Ordering process is a redundant activity under strategy NS, which increases the total lead time and the retailer's inventory risk. Nevertheless, the retailer's inventory is managed by the upstream manufacturer under strategy IS. Ordering process is omitted, so total lead time and short cost decrease. Hence, the negative impact of ordering process uncertainty can be reduced if strategy IS is utilized, especially under high uncertainty level. It is profitable for the whole supply chain to share information when the ordering process time exists.
The effect of transportation time uncertainty on supply chain costs is depicted in Figure 12 operations cost owing to the internal risk. Moreover, while the cost is less for strategy IS, the value of IS is not remarkable. After all, the uncertainty in transport cannot be eliminated in the spite of shared information. Consequently, it is hard to control the risk caused by uncertain transportation.

Conclusions
This paper studies an information sharing strategy in a multilevel supply chain with one manufacturer, one carrier, and one retailer, where all members have to be confronted with uncertain yield, demand, and lead time in a complex multiperiod environment. Two strategies can be adopted to react to multiple uncertainties: IS or NS. Each member is regarded as an adaptive agent, where decisions can be adjusted in each period to dynamically adapt to the external situation. The costs of supply chain and channel members under two strategies are contrasted, and the effects of yield, demand, and lead time uncertainties on the two strategies are investigated. We find: (i) strategy IS is optimal for the upstream manufacturer under uncertain yield or demand; (ii) but for the whole supply chain, the retailer, and the carrier, strategy IS is not always the suitable choice; information sharing should be avoided when demand, yield, or transportation time uncertainty is large; (iii) the increase of transportation time uncertainty benefits the retailer; (iv) for the whole supply chain, the cost from ordering process uncertainty is cut down evidently through sharing information; however, it is not easy to mitigate the uncertain transportation risk with sharing information.
There are several directions for future research. First, the manufacturer's capacity is infinite. This assumption could be relaxed to study a more complex case, where the manufacturer may be faced with capacity crisis. Second, it is worth studying the impact of other decision adjustment methods on information sharing behavior. Third, market and inventory information are shared among the supply chain members in this paper, but the yield risk upstream is not shared. The factor can be further considered and studied.

Data Availability
My data is public.

Conflicts of Interest
The authors declare that they have no conflicts of interest.