Pricing and strategy selection in a closed-loop supply chain under demand and return rate uncertainty

Closed-loop supply chain (CLSC) decision-making involves many uncertainties, which makes the decision-making process more complex and diversified. This study considered a two-stage CLSC consisting of an original manufacturer and a third-party recycler. Without any government policy support, considering the effects of market demand, product return rate, and consumer perceived value, a CLSC decision model based on market demand with a [0,1] distribution was established. The model analyzes three situations—a manufacturer monopoly, the Cournot duopoly game, and the Stackelberg competition game—and solves them. The optimal values of decision variables such as optimal pricing, market demand, and all parties’ profits in the CLSC are obtained, and a strict mathematical proof is given. Through the model-solving process, the effects of product return rate and consumer perceived value on decision variables are analyzed; then, the profit allocation between the original manufacturer and the third-party recycler under different cooperation modes is analyzed. In addition, the four combinations of competition and cooperation are analyzed based on game theory. The Nash equilibrium solution and Pareto optimal solution of the four modes are analyzed by drawing a bimatrix Nash equilibrium table. The results indicate that the cooperation–cooperation mode is difficult to produce automatically, and government policy guidance and support are often needed to achieve Pareto optimality. Finally, a numerical example is given to validate the proposed model. In this way, the proposed model provides reliable theoretical support for the decision-making of both sides in a CLSC.

     

Sourcing decision under disruption risk with supply and demand uncertainty: A newsvendor approach

Multi-sourcing is considered as a common practice to hedge against supply disruption risk. In this context, this paper proposes two models for optimal order allocation in newsvendor setting, where both supply and demand are uncertain. The first model considers a risk neutral decision maker who maximizes the total expected profit under disruption risk. The second one is for a risk averse decision maker who does so under service level constraints. Analytical closed form solutions for both the models are derived. To overcome the computational complexity of the exact optimal solution, two algorithms are developed to generate optimal order quantity and the corresponding set of suppliers. The solutions with exact optimization algorithms and the proposed ones are illustrated and compared with numerical examples. The results show that the proposed algorithms give the exact optimal solution while being tractable. Finally, a case study is used to illustrate the applicability of the proposed model.     

Investigation of rolling horizon flexibility contracts in a supply chain under highly variable stochastic demand

Email: patrick.walsh{at}ul.ie Received on 19 January 2007. Accepted on 3 October 2007. A discrete-event simulation model of a supply chain has beendeveloped to evaluate operational performance of sharing uncertaininformation on upcoming demand between an original equipmentmanufacturer (OEM) and a contract manufacturer under a formalrolling horizon flexibility (RHF) contract in a four-node supplychain. There are two types of RHF contracts evaluated, i.e.RHF contract with constant flexibility and decreasing flexibilitybounds. The demand is externalized (i.e. the OEM receives thedemand), stochastic and generated according to a gamma distribution.This paper reports on the analysis of RHF contracts operatingwith coefficients of variation of demand up to 2.00. Analysisof the interaction of RHF contracts with forecasting and theimpact an RHF contract has on the transmission of the bullwhipeffect are reported here.     

Long-term and penalty contracts in a two-stage supply chain with stochastic demand

Recent applications of game-theoretic analysis to supply chain efficiency have focused on constructs between a buyer (the retailer or manufacturer) and a seller (the supplier) in successive stages of a supply chain. If demand for the final product is stochastic then the supplier has an incentive to keep its capacity relatively low to avoid creating unneeded capacity. The manufacturer, on the other hand, prefers the supplier’s capacity to be high to ensure that the final demand is satisfied. The manufacturer therefore constructs a contract to induce the supplier to increase its production capacity. Most research examines contracting when final demand is realized after the manufacturer places its order to the supplier. However, if final demand is realized before the manufacturer places its order to the supplier, these types of contracts can be ineffective. This paper examines two contracts under the latter timing scenario: long-term contracts in which the business relationship is repeated, and penalty contracts in which the supplier is penalized for too little capacity. Results indicate long-term contracts increase the profit potential of the supply chain. Furthermore, the penalty contracts can ensure that the supplier chooses a capacity level such that the full profit potential is achieved.     

Managing the supply and demand uncertainty in workforce recruitment: planned or just-in-time acquisition

Managing knowledge workers is highly complex because of the need to balance the costs associated with their training and holding costs against the need to meet market demand as quickly as possible. Unlike previous approaches to this problem in the workforce management literature, this paper develops a stochastic optimization model to examine the impact of not only uncertainty of the demand of knowledge services but also that of the supply of knowledge workers on a recruiting strategy. Hypotheses on optimal recruiting decisions that this paper suggests include: (1) high holding and training costs decrease recruitment of apprentices; (2) high mobility of skilled workers decreases recruitment of apprentices; (3) high elasticity of the supply of skilled workers decreases recruitment of apprentices; (4) high volatility of the demand of knowledge services decreases recruitment of apprentices; and (5) in high seasonal effect on the demand, the decision policy based on decision thresholds proportional to seasonal demands outperforms the decision policy based on a constant decision threshold. Suggested hypotheses are supported by a simulation of the model. Model parameters in the simulation are estimated based on the survey of information security consulting service companies in South Korea.     

Dynamic dairy facility location and supply chain planning under traffic congestion and demand uncertainty: A case study of Tehran

In this paper, dynamic dairy facility location and supply chain planning are studied through minimizing the costs of facility location, traffic congestion and transportation of raw/processed milk and dairy products under demand uncertainty. The proposed model dynamically incorporates possible changes in transportation network, facility investment costs, monetary value of time and changes in production process. In addition, the time variation and the demand uncertainty for dairy products in each period of the planning horizon is taken into account to determine the optimal facility location and the optimal production volumes. Computational results are presented for the model on a number of test problems. Also, an empirical case study is conducted in order to investigate the dynamic effects of traffic congestion and demand uncertainty on facility location design and total system costs.     

Optimal promotion planning—depth and frequency—for a two-stage supply chain under Markov switching demand

In considering the retailer–supplier supply chain, this paper analyzes how a retailer reasonably decides both the depth and frequency of the price discount promotion including or excluding a supplier’s inventory decision. Assuming that the promotion frequency used by the retailer is probabilistic, we model a promotion-inventory decision under an AR(1) demand with a Markov switching promotion regime. After obtaining the optimal promotion plan, our analysis also considers the behavior of the optimal promotion decision; the retailer’s price format selection, either an Every-Day-Low-Price policy (EDLP) or a Promotion policy (HiLo); and the impact of information sharing of promotion status on the system’s performance. Our results suggest that a retailer tends to overpromote if inventory cost is excluded in its promotion decision, that increasing the market share is a preferable action for both the retailer and the supplier, that total margin and price-elasticity play an important role in selecting the price format, and that the profitability for a supplier of sharing promotion information depends on the transition probabilities of the Markov switching regime.     

Two-period pricing and decision strategies in a two-echelon supply chain under price-dependent demand

This paper presents a two-period supply chain model which is comprised of one manufacturer and one retailer who are involved in trading a single product. The demand rate in each period is dependent on the selling prices of the current period and the previous period. We assume that the manufacturer acts as the Stackelberg leader and declares wholesale price(s) to the retailer who follows the manufacturer’s decision and sets his selling prices for two consecutive periods. The manufacturer adopts one of the two pricing options: (1) setting the same wholesale price to both the selling periods (2) setting different wholesale prices to two different selling periods. Based on these pricing options, we develop four decision strategies of the manufacturer and the retailer and compare them. For a numerical example, we study the effects of these decision strategies on the optimal results of the supply chain. Further, we graphically analyze under what circumstances a particular decision strategy plays a dominant role.     

Reliability-based user equilibrium in a transport network under the effects of speed limits and supply uncertainty

This study investigates the system-wide traffic flow re-allocation effect of speed limits in uncertain environments. Previous studies have only considered link capacity degradation, which is only one of the factors that lead to supply uncertainty. This study examines how imposing speed limits reallocates the traffic flows in a situation of general supply uncertainty with risk-averse travelers. The effects of imposing a link-specific speed limit on link driving speed and travel time are analyzed, given the link travel time distribution before imposing the speed limit. The expected travel time and travel time standard deviation of a link with a speed limit are derived from the link travel time distribution and are both continuous, monotone, and convex functions in terms of link flow. A distribution-free, reliability-based user equilibrium with speed limits is established, in which travelers are assumed to choose routes that minimize their own travel time budget. A variational inequality formulation for the equilibrium problem is proposed and the solution properties are provided. In this study, the inefficiency of a reliability-based user equilibrium flow pattern with speed limits is defined and found to be bounded above when supply uncertainty refers to capacity degradation. The upper bound depends on the level of risk aversion of travelers, a ratio related to the design and worst-case link capacities, and the highest power of all link performance functions.     

Modelling and computing (Rn, Sn) policies for inventory systems with non-stationary stochastic demand

This paper addresses the single-item, non-stationary stochastic demand inventory control problem under the non-stationary (R, S) policy. In non-stationary (R, S) policies two sets of control parameters—the review intervals, which are not necessarily equal, and the order-up-to-levels for replenishment periods—are fixed at the beginning of the planning horizon to minimize the expected total cost. It is assumed that the total cost is comprised of fixed ordering costs and proportional direct item, inventory holding and shortage costs. With the common assumption that the actual demand per period is a normally distributed random variable about some forecast value, a certainty equivalent mixed integer linear programming model is developed for computing policy parameters. The model is obtained by means of a piecewise linear approximation to the non-linear terms in the cost function. Numerical examples are provided.     

Remarks on the optimization method of a manufacturing system with stochastic breakdown and rework process in supply chain management

Chiu et al. (2010) [8] present the proof of convexity of the long-run average cost function E[TCU(t₁)] for a manufacturing system with stochastic breakdown and rework process. This note not only demonstrates that E[TCU(t₁)] is not convex but also adopts the rigorous methods of mathematics to develop the complete solution procedure to find the optimal solution for removing shortcomings of the above paper mentioned.     

Determining the reorder point and order-up-to level to satisfy two constraints in a periodic review system under negative binomial demand

In this paper we consider an inventory management problem motivated by a specific practical context that concerns the commonly used periodic review, reorder point, order-up-to-level control system. In particular, the reorder point and order-up-to level have to be selected so as to satisfy two management-specified constraints. First, from a marketing (or, more generally, a business) perspective, the actual fill rate achieved must be no lower than a prescribed value. Second, for production or supply purposes, the average time between consecutive replenishments must be as close as possible to a target value. The demand distribution considered is the negative binomial. An efficient procedure is developed with illustrations.     

Trade credit competition between two retailers in a supply chain under credit-linked retail price and market demand

The paper considers a supply chain system in which the sole manufacturer supplies the same product to two retailers who compete in offering trade credit period to customers. Both the market demand and retail prices vary with the trade credit periods offered by the retailers. The manufacturer also provides a trade credit period to both the retailers to settle down their accounts. The net profit function of the supply chain is derived considering possible relationships among the trade credit periods offered by the manufacturer and the retailers and the time when each retailer receives the last payment from his customer. An algorithm is developed to find the optimal solution of the proposed model. From the numerical study, it is observed that a two-level trade credit financing can increase profits not only for the manufacturer and the retailers but also for the whole supply chain.     

Manufacturer’s return policy in a two-stage supply chain with two risk-averse retailers and random demand

This paper studies the manufacturer’s return policy and the retailers’ decisions in a supply chain consisting of one manufacturer and two risk-averse retailers under a single-period setting with price-sensitive random demand. We characterize each retailer’s risk-embedded objective via conditional value-at-risk, and construct manufacturer-Stackelberg games with and without horizontal price competition between the retailers. We explore, through numerical studies, the effects of the retailers’ aversion to risk and other parameters on the manufacturer’s return policy and profit and the retailers’ decisions. We further investigate the effect of distribution asymmetry by comparing the results with normal and lognormal demand.     

An approach to find redundant objective function(s) and redundant constraint(s) in multi-objective nonlinear stochastic fractional programming problems

Structural redundancies in mathematical programming models are nothing uncommon and nonlinear programming problems are no exception. Over the past few decades numerous papers have been written on redundancy. Redundancy in constraints and variables are usually studied in a class of mathematical programming problems. However, main emphasis has so far been given only to linear programming problems. In this paper, an algorithm that identifies redundant objective function(s) and redundant constraint(s) simultaneously in multi-objective nonlinear stochastic fractional programming problems is provided. A solution procedure is also illustrated with numerical examples. The proposed algorithm reduces the number of nonlinear fractional objective functions and constraints in cases where redundancy exists.     

The simplified solution procedure for deteriorating items under stock-dependent demand and two-level trade credit in the supply chain management

Min et al. [1] (J. Min, Y.W. Zhou, J. Zhao, An inventory model for deteriorating items under stock-dependent demand and two-level trade credit, Appl. Math. Model. 34 (2010) 3273–3285.) develop an inventory model for deteriorating items under stock-dependent demand and two-level trade credit. They provide the necessary and sufficient conditions of the existence and uniqueness of the optimal solutions that could maximize the retailer’s average profit per unit time. Basically, their paper is correct and interesting. Recently, several researchers have been showing a huge interest in developing simple and easy to implement solution procedures in management science. Therefore this paper indicates that Min et al.’s solution procedure can be further improved and simplified. So, the main purpose of this paper is to present simple and easy to understand solution procedures to locate the optimal solutions of an inventory model that considers deteriorating items under stock-dependent demand and two-level trade credit.     

A comparison between the order and the volume fill rate for a base-stock inventory control system under a compound renewal demand process

The order fill rate (OFR) is sometimes suggested as an alternative to the volume fill rate (VFR) (most often just denoted fill rate) as a performance measure for inventory control systems. We consider a continuous review, base-stock policy, where replenishment orders have a constant lead time and unfilled demands are backordered. For this policy, we develop exact mathematical expressions for the two fill-rate measures when demand follows a compound renewal process. We also elaborate on when the OFR can be interpreted as the (extended) ready rate. For the case when customer orders are generated by a negative binomial distribution, we show that it is the size of the shape parameter of this distribution that determines the relative magnitude of the two fill rates. In particular, we show that when customer orders are generated by a geometric distribution, the OFR and the VFR are equal.     

Clusters in a group: Decision making in the vector space formulation of the analytic hierarchy process

For a large group that might have a clustered structure, we discuss and implement an algorithm to group individuals into natural clusters using a convenient similarity measure. The cohesiveness of a homogeneous group or cluster is also investigated.