The impact of decision timing on the suppliers’ interactions: simultaneous moves <Emphasis Type="Italic">versus</Emphasis> sequential moves

The last few decades have witnessed a huge growth of outsourcing in industry where the downstream firm assigns its production tasks to different upstream suppliers. This makes the supply chain structure more complicated and gives rise to some relevant operational questions. This paper focuses on a supply chain structure that consists of one assembler and two suppliers, and both suppliers’ production yields are stochastic. The assembler delegates the quantity decisions to the suppliers, and the two suppliers choose their production quantities either simultaneously or sequentially. We compare the suppliers’ equilibrium production strategies under these two scenarios. Our results show that the decision sequence can exert significant influences on the firm’s and channel’s equilibrium payoffs. At any given wholesale price, both suppliers produce more components under sequential moves than under simultaneous moves, and this results in higher payoffs for the suppliers, the assembler and the entire supply chain. The supplier’s profit increases if he can make the decision later under sequential moves. From the channel’s perspective, it is more beneficial for the supplier with a higher production cost to make the decision first. The assembler is able to extract more surplus by endogenously setting the wholesale price. However, this may make the suppliers worse off under sequential moves than under simultaneous moves.     

Allocating flexible servers in serial systems with switching costs

Consider a firm that operates a make-to-order serial production system and employs a cross-trained workforce. We model such a firm as a tandem queuing system in which flexible servers can be allocated across stations, and assume that a switching cost is charged when servers move between stations. We show that even in the two-station two-server case the optimal policy follows a complex state-dependent structure that may be difficult to implement in practice. We propose three alternate heuristic policies and assess their performance. We show that a simpler policy which only moves one server can achieve close to optimal results.     

Flexible capacity strategy with multiple market periods under demand uncertainty and investment constraint

We establish a flexible capacity strategy model with multiple market periods under demand uncertainty and investment constraints. In the model, a firm makes its capacity decision under a financial budget constraint at the beginning of the planning horizon which embraces n market periods. In each market period, the firm goes through three decision-making stages: the safety production stage, the additional production stage and the optimal sales stage. We formulate the problem and obtain the optimal capacity, the optimal safety production, the optimal additional production and the optimal sales of each market period under different situations. We find that there are two thresholds for the unit capacity cost. When the capacity cost is very low, the optimal capacity is determined by its financial budget; when the capacity cost is very high, the firm keeps its optimal capacity at its safety production level; and when the cost is in between of the two thresholds, the optimal capacity is determined by the capacity cost, the number of market periods and the unit cost of additional production. Further, we explore the endogenous safety production level. We verify the conditions under which the firm has different optimal safety production levels. Finally, we prove that the firm can benefit from the investment only when the designed planning horizon is longer than a threshold. Moreover, we also derive the formulae for the above three thresholds.     

Compensation plan for competing salespersons under asymmetric information

We investigate the optimal compensation scheme involving one firm and two competing salespersons deployed in different territories under asymmetric information. The problem is analyzed using a two-stage game. In the first stage, the firm announces the compensation plans. The two salespersons, who are closer to customers, have superior market information and then simultaneously but independently decide which plans to sign. The firm decides the production quantity and the salespersons independently make effort decisions. In the second stage, sales volumes are realized and the associate payments are made.     

The cover pebbling number of graphs

A pebbling move on a graph consists of taking two pebbles off of one vertex and placing one pebble on an adjacent vertex. In the traditional pebbling problem we try to reach a specified vertex of the graph by a sequence of pebbling moves. In this paper we investigate the case when every vertex of the graph must end up with at least one pebble after a series of pebbling moves. The cover pebbling number of a graph is the minimum number of pebbles such that however the pebbles are initially placed on the vertices of the graph we can eventually put a pebble on every vertex simultaneously. We find the cover pebbling numbers of trees and some other graphs. We also consider the more general problem where (possibly different) given numbers of pebbles are required for the vertices.     

Dynamic pricing with uncertain production cost: An alternating-move approach

This article studies a two-firm dynamic pricing model with random production costs. The firms produce the same perishable products over an infinite time horizon when production (or operation) costs are random. In each period, each firm determines its price and production levels based on its current production cost and its opponent’s previous price level. We use an alternating-move game to model this problem and show that there exists a unique subgame perfect Nash equilibrium in production and pricing decisions. We provide a closed-form solution for the firm’s pricing policy. Finally, we study the game in the case of incomplete information, when both or one of the firms do not have access to the current prices charged by their opponents.     

Resolution approach for multi-objective problems with uncertain demands

The job-shop scheduling problem (JSP) is one of the hardest problems (NP-complete problem). In a lot of cases, the combination of goals and resource exponentially increases search space. The objective of resolution of such a problem is generally, to maximize the production with a lower cost and makespan. In this paper, we explain how to modify the objective function of genetic algorithms to treat the multi-objective problem and to generate a set of diversified “optimal” solutions in order to help decision maker. We are interested in one of the problems occurring in the production workshops where the list of demands is split into firm (certain) jobs and predicted jobs. One wishes to maximize the produced quantity, while minimizing as well as possible the makespan and the production costs. Genetic algorithms are used to find the scheduling solution of the firm jobs because they are well adapted to the treatment of the multi-objective optimization problems. The predicted jobs will be inserted in the real solutions (given by genetic algorithms). The solutions proposed by our approach are compared to the lower bound of the cost and makespan in order to prove the quality and robustness of our proposed approach.     

Dynamic pricing with real-time demand learning

In many service industries, the firm adjusts the product price dynamically by taking into account the current product inventory and the future demand distribution. Because the firm can easily monitor the product inventory, the success of dynamic pricing relies on an accurate demand forecast. In this paper, we consider a situation where the firm does not have an accurate demand forecast, but can only roughly estimate the customer arrival rate before the sale begins. As the sale moves forward, the firm uses real-time sales data to fine-tune this arrival rate estimation. We show how the firm can first use this modified arrival rate estimation to forecast the future demand distribution with better precision, and then use the new information to dynamically adjust the product price in order to maximize the expected total revenue. Numerical study shows that this strategy not only is nearly optimal, but also is robust when the true customer arrival rate is much different from the original forecast. Finally, we extend the results to four situations commonly encountered in practice: unobservable lost customers, time dependent arrival rate, batch demand, and discrete set of allowable prices.     

Managing new and differentiated remanufactured products

We study a firm that makes new products in the first period and uses returned cores to make remanufactured products (along with new products) in future periods. The remanufactured product is differentiated from the new product, so the firm needs to choose differentiated prices. We analyze the monopoly environment in two-period, multi-period (three, four and five) and infinite planning horizons, and characterize the optimal remanufacturing and pricing strategy for the firm. In the process, we identify remanufacturing savings thresholds that determine the production and pricing strategy for the firm. Among other results, we find—counter to intuition—that in a finite-horizon, multi-period setting, the optimal policy is not necessarily monotone in remanufacturing savings.     

The optimal resource portfolio under consumer choice and demand risk for vertically differentiated products

We study the optimal resource portfolio of a firm that sells two vertically differentiated products and utilizes resource flexibility and responsive pricing. We model this decision problem as a two-stage stochastic programming problem with recourse: In the first stage, the firm determines its resource mix and capacities so as to maximize the expected profit under demand uncertainty; in the second stage, uncertainty is resolved and the firm determines its production and pricing decision, constrained by its investment decision. We show that the objective function of this decision problem is not well-behaved (ie, it may have multiple local maxima). Using the concept of Pareto dominance, we reduce the feasible investment region, without loss of optimality, to one in which the objective function is well-behaved everywhere. This reduction allows us to derive the necessary and sufficient conditions for the optimal capacity decision and to gain insights.     

Cooperation between strands of practice: challenges and opportunities for the renewal of OR

Collaboration between OR groups following different ‘strands of practice’, namely adhering to different ways of conducting OR practice, is difficult. We demonstrate the existence of this problem in two contexts. Firstly, we found several different strands of practice within an independent, entrepreneurial OR firm. Though these strands had the potential to be highly complementary, their co-existence within one firm led to serious tensions and their potential synergy has not yet been realised. When the independent OR firm achieved successful renewal by transforming one of their strands of practice into a new approach to projects, this very success created a new set of competitive challenges. Secondly, an independent OR consulting firm working with a client's internal research group found that the latter's approach conflicted with its own, resulting in an unsuccessful project. We conclude that the ‘micro-level’ problems of collaboration between individual practitioners and between groups, though largely neglected in the OR literature, can be serious impediments to success and renewal of OR practice.     

Edit distance with move operations

The traditional edit-distance problem is to find the minimum number of insert-character and delete-character (and sometimes change character) operations required to transform one string into another. Here we consider the more general problem of a string represented by a singly linked list (one character per node) and being able to apply these operations to the pointer associated with a vertex as well as the character associated with the vertex. That is, in O(1) time, not only can characters be inserted or deleted, but substrings can be moved or deleted. We limit our attention to the ability to move substrings and leave substring deletions for future research. Note that O(1) time substring move operation implies O(1) substring exchange operation as well, a form of transformation that has been of interest in molecular biology. We show that this problem is NP-complete, and that a “recursive” sequence of moves can be simulated with at most a constant factor increase by a non-recursive sequence. Although a greedy algorithm is known to have poor (a polynomial factor) worst case performance, we present a polynomial time greedy algorithm for non-recursive moves which on a subclass of instances of a problem of size n achieves an approximation factor to optimal of at most O(logn). The development of this greedy algorithm shows how to reduce moves of substrings to moves of characters, and how to convert moves of characters to only inserts and deletes of characters.     

Global facility network design in the presence of competition

We study the facility network design problem for a global firm that is a monopolist seller in its domestic market but faces local competition in its foreign market. The global firm produces in the face of demand and exchange rate uncertainty but can postpone localization and distribution of the output until after uncertainties are resolved. The competitor in the foreign market, however, enjoys the flexibility of postponing all production activities until after uncertainties are resolved. The two firms engage in an ex-post Cournot competition in the foreign market. We consider three potential network configurations for the global firm. Under a linear demand function, we provide the necessary and sufficient condition that one of the three networks is the global firm’s optimal choice, and explore how the presence of foreign competition affects the sensitivity of the global firm’s design to various cost parameters and market uncertainties.     

The more the better? Optimal degree of supply-chain cooperation between competitors

We consider the outsourcing strategy problem of two competing original equipment manufacturers (OEMs) whose products are each made up of two components. The OEMs have different specializations, and therefore the component that each firm can produce in-house is different. Each firm must decide whether to outsource the other component to the competing OEM or to a third-party supplier. Prior research has demonstrated that competitors can be better off cooperating as supply-chain partners; therefore, one might expect that, as long as the OEMs are not at a severe cost disadvantage, they should maximize their cooperation as supply-chain partners, especially when competition between products is strong. Interestingly, this study finds that more cooperation between competitors may actually be harmful. Under certain conditions, while one of the OEMs should outsource to the competing firm, the other should outsource to a third-party supplier, even when the third-party supplier is more expensive and the competition is intense.     

Environmental safety stock: The impacts of regulatory and voluntary control policies on production planning,inventory control,and environmental performance

This paper analyzes the impacts of different pollution control policies on a firm’s decisions of production planning and inventory control. Based on a stochastic model with both demand and environmental uncertainties, we derive the optimal policies of production planning and inventory control under both regulatory and voluntary pollution control approaches, and investigate their operational and environmental effects. We establish that the conventional wisdom which suggests that reduction of environmental waste at the end of a production process also decreases the stock and throughput levels of a production system is not necessarily true. Rather, a regulatory environmental standard that limits the total amount of waste may induce the firm to raise its planned stock level, which would lead to a higher expected amount of environmental wastes before the standard is enforced as well as environmental risks at other stages of the production process. The additional planned stock level, which is termed “environmental safety stock,” can be reversed by using the voluntary control approach that provides the firm with the flexibility to occasionally exceed the environmental standard. We also conduct numerical experiments to analyze the effects of different values of model parameters under different control approaches. The analytical results provide new insights to the impacts of a firm’s production and inventory decisions on the natural environment as well as to the choices of pollution control approaches by decision makers in both the private and public sectors.     

Environmental considerations on the optimal product mix

Several types of regulations limit the amount of different emissions that a firm may create from its production processes. Depending on the emission, these regulations could include threshold values, penalties and taxes, and/or emission allowances that can be traded. However, many firms try to comply with these regulations without a systematic plan, often leading not only to emission violations and high penalties, but also to high costs. In this paper, we present two mathematical models that can be used by firms to determine their optimal product mix and production quantities in the presence of several different types of environmental constraints, in addition to typical production constraints. Both models are comprehensive and incorporate several diverse production and environmental issues. The first model, which assumes that each product has just one operating procedure, is a linear program while the second model, which assumes that the firm has the option of producing each product using more than one operating procedure, is a mixed integer linear program. The solutions of both models identify the products that the firm should produce along with their production quantities. These models can be used by firms to quickly analyze several “what if” scenarios such as the impact of changes in emission threshold values, emission taxes, trading allowances, and trading transaction costs.     

Stochastically dominating shifts and the competitive firm

The production responses of the competitive firm to stochastically dominating shifts in the distribution of output-price have been the object of much research. In a recent paper, Simpson and Sproule [Metroeconomica 51 (2) (2000) 168–181] present five sets of sufficient conditions, any one of which may be used to jointly sign the production responses of the competitive firm to first-, second-, and third-order stochastically dominating shifts. This paper demonstrates that one of the conditions outlined in the above mentioned reference is unnecessarily restrictive in the case of the logarithmic and the positive-power utility functions.     

Maximum-revenue tariff under Bertrand duopoly with unknown costs

This paper considers an international trade under Bertrand model with differentiated products and with unknown production costs. The home government imposes a specific import tariff per unit of imports from the foreign firm. We prove that this tariff is decreasing in the expected production costs of the foreign firm and increasing in the production costs of the home firm. Furthermore, it is increasing in the degree of product substitutability. We also show that an increase in the tariff results in both firms increasing their prices, an increase in both expected sales and expected profits for the home firm, and a decrease in both expected sales and expected profits for the foreign firm.     

规模效应下产品具有可替代性的竞争企业的外包决策

针对产品具有一定替代性的两个竞争企业(分别为企业1和企业2)和存在规模效应的上游供应商的外包决策问题, 构建了企业1 外包前后各方的利润模型,求解了下游企业的外包和自产的最优策略以及供应商的最佳批发价格,分析了企业1 的外包策略对企业2 和供应商的外包决策的影响,比较了产品替代性对外包前后各决策变量的影响。研究发现:当企业的单位生产成本高于外包成本时,企业也可能选择自产;而当企业的单位生产成本低于外包成本时,企业也可能选择产品外包。并对模型进行进一步的拓展,比较了下游企业作顺序和同时外包决策两种情景的异同。     

The setting of profit targets for target oriented divisions

Setting profit targets and striving to achieve them is fundamental to business survival and success. However, there has been little research on modeling profit-target setting. In this paper, we study analytic target setting under a common business scenario where a firm is in control of multiple divisions. Both the firm and the divisions maximize the profit probability, i.e., the probability of achieving some given profit target. The firm sets a profit target for each division which then acts as a price-setting newsvendor. We first obtain the optimal order quantity, the optimal retail price, and the maximal profit probability of a single division given its assigned target. We then derive the firm’s profit probability and focus on two specific cases to gain more managerial insights. In the first case of fair target setting, we show that when each division’s demand distribution has an increasing failure rate, if a division has a relatively high (low) production cost, its assigned profit target decreases (increases) with regard to its price elasticity. In the second case, if the firm is in control of two identical divisions, each division’s optimal profit target is just half of the firm’s profit target when the price elasticity is two or more, regardless of production cost and demand distribution.