Lot sizing and unequal-sized shipment policy for an integrated production-inventory system

This article develops a single-manufacturer single-retailer production-inventory model in which the manufacturer delivers the retailer’s ordered quantity in unequal shipments. The manufacturer’s production process is imperfect and it may produce some defective items during a production run. The retailer performs a screening process immediately after receiving the order from the manufacturer. The expected average total cost of the integrated production-inventory system is derived using renewal theory and a solution procedure is suggested to determine the optimal production and shipment policy. An extensive numerical study based on different sets of parameter values is conducted and the optimal results so obtained are analysed to examine the relative performance of the models under equal and unequal shipment policies.     

Three stage trade credit policy in a three-layer supply chain–a production-inventory model

The main purpose of this paper is to investigate the optimal replenishment lot size of supplier and optimal production rate of manufacturer under three levels of trade credit policy for supplier–manufacturer–retailer supply chain. The supplier provides a fixed credit period to settle the accounts to the manufacturer, while the manufacturer gives a fixed credit period to settle the account to the retailer and the retailer, in turn, also offers a credit period to each of its customers to settle the accounts. We assume that the supplier supplies the raw material to the manufacturer and sends back the defective raw materials to the outside supplier after completion of inspection at one lot with a sales price. The system always produces good items in the model. Also, we consider the idle times of supplier and manufacturer. Finally, numerical examples are provided to illustrate the behaviour and application of the model with graphical simulation.     

The optimal integrated inventory policy with price-and-credit-linked demand under two-level trade credit

In this paper, we proposed a generalized, integrated, supplier–retailer inventory model using a trade credit policy. The trade credit policy adopted here is a two-level trade credit policy in which the supplier offers the retailer a permissible delay period M, and the retailer in turn provides customers a permissible delay period N. Cases where M > N and M ? N are explored thoroughly. In addition, the demand rate is assumed to be a function of both retail price and the customers’ credit period. Consequently, this paper deals with the problem of determining the optimal retail price, economic order quantity, and the number of shipments from the supplier to the retailer in one production run for an integrated inventory system under both two-level trade credit and price-and-credit-linked demand rate. Algorithms are developed in order to determine the joint optimal policies. Numerical examples are presented to illustrate the proposed models, as well as sensitivity analysis of key parameters.     

Commitment decisions with demand information updating and a capital‐constrained supplier

In this paper, we study a single two‐echelon supply chain with a capital‐constrained supplier (manufacturer) and a retailer. The supply chain faces a stochastic demand. As the production lead time is long, the market demand is updated during the supplier's production lead time. The supplier needs to determine the production quantity based on the original demand forecast, and the retailer needs to determine the time and quantity to order. The retailer can place an order before the supplier's production (preorder) or after the supplier's production (regular order). We prove the existence of optimal equilibrium solutions under both preorder and regular order strategies. We analytically investigate the order strategies for the supply chain agents under perfect and worthless market information updating. Moreover, we numerically analyze the impact of the information updating quality on the order strategy selection, and the effect of exogenous shocks on the supply chain agents.     

Analysis of the maximum level policy in a production-distribution system

We consider a production-distribution system, where a facility produces one commodity which is distributed to a set of retailers by a fleet of vehicles. Each retailer defines a maximum level of the inventory. The production policy, the retailers replenishment policies and the transportation policy have to be determined so as to minimize the total system cost. The overall cost is composed by fixed and variable production costs at the facility, inventory costs at both facility and retailers and routing costs. We study two different types of replenishment policies. The well-known order-up to level (OU) policy, where the quantity shipped to each retailer is such that the level of its inventory reaches the maximum level, and the maximum level (ML) policy, where the quantity shipped to each retailer is such that the inventory is not greater than the maximum level. We first show that when the transportation is outsourced, the problem with OU policy is NP-hard, whereas there exists a class of instances where the problem with ML policy can be solved in polynomial time. We also show the worst-case performance of the OU policy with respect to the more flexible ML policy. Then, we focus on the ML policy and the design of a hybrid heuristic. We also present an exact algorithm for the solution of the problem with one vehicle. Results of computational experiments carried out on small size instances show that the heuristic can produce high quality solutions in a very short amount of time. Results obtained on a large set of randomly generated problem instances are also shown, aimed at comparing the two policies.     

Design of Stochastic Distribution Networks Using Lagrangian Relaxation

This paper addresses the design of single commodity stochastic distribution networks. The distribution network under consideration consists of a single supplier serving a set of retailers through a set of distribution centers (DCs). The number and location of DCs are decision variables and they are chosen from the set of retailer locations. To manage inventory at DCs, the economic order quantity (EOQ) policy is used by each DC, and a safety stock level is kept to ensure a given retailer service level. Each retailer faces a random demand of a single commodity and the supply lead time from the supplier to each DC is random. The goal is to minimize the total location, shipment, and inventory costs, while ensuring a given retailer service level. The introduction of inventory costs and safety stock costs leads to a nonlinear NP-hard optimization problem. A Lagrangian relaxation approach is proposed. Computational results are presented and analyzed showing the effectiveness of the proposed approach.     

Joint shipment consolidation and inventory decisions in a two-stage distribution system

This study is motivated by a problem that an industrial distributorship faced while distributing automotive spare parts to service and repair centers. Considering the problem encountered, we present an analytical model for joint inventory and shipment consolidation decisions in a two-stage distribution system with a single distribution center, multiple non-identical retailers, and an outside supplier. The retailers face stochastic end-customer demand and use continuous review to replenish inventories. On the other hand, the distribution center uses a periodic review policy and employs a time-based shipment consolidation policy to dispatch retailers’ accumulated orders at the end of each consolidation cycle. We present an exact optimization technique to compute the optimal replenishment quantity at the distribution center, order-up-to level at retailers, and a shipment consolidation cycle length to measure the effects of inventory at retailers on the overall performance. Finally, we perform numerical experiments to measure the impact of various parameters on the overall distribution system.     

风险规避零售商期末二次订购的供应链决策模型

以风险规避零售商和风险规避供应商组成的两层供应链系统为研究对象, 在条件风险估值的风险度量准则下讨论两生产模式下风险规避零售商的最优订购策略和风险规避供应商的最优生产策略. 通过数值实验得出如下结论: 若零售商的风险规避度越小, 则零售商的第1 次最优订购量越多, 风险利润越大; 供应商的第1 次最优生产量随着供应商的风险规避度减小而增大; 零售商的风险规避度越小, 越不利于供应商的生产投机行为.

     

A decision rule for coordination of inventory and transportation in a two-stage supply chain with alternative supply sources

This paper deals with a two-stage supply chain that consists of two distribution centers and two retailers. Each member of the supply chain uses a (Q,R) inventory policy, and incurs standard inventory holding and backlog costs, as well as ordering and transportation costs. The distribution centers replenish their inventory from an outside supplier, and the retailers replenish inventory from one of the two distribution centers. When a retailer is ready to replenish its inventory that retailer must decide whether it should replenish from the first or second distribution center. We develop a decision rule that minimizes the total expected cost associated with all outstanding orders at the time of order placement; the retailers then repeatedly use this decision rule as a heuristic. A simulation study which compares the proposed policy to three traditional ordering policies illustrates how the proposed policy performs under different conditions. The numerical analysis shows that, over a large set of scenarios, the proposed policy outperforms the other three policies on average.     

Supply chain financing with advance selling under disruption

We study a financing problem in a supply chain (SC) consisting of one supplier and one buyer under supply disruption. The supplier could face a disruption at its end which could effectively reduce its yield in case of disruption, thereby resulting in supply yield uncertainty. The retailer can finance the supplier using advance selling that can help mitigate the impact of disruption. We model this problem as a Stackelberg game, where the supplier as the leader announces the wholesale price and the retailer responds by deciding its optimal order quantity given stochastic demand and an exogenous fixed retail price. The supplier then commences production and a disruption can happen with a known probability. We assume that under disruption the quantity delivered is a fraction of the initial quantity ordered by the retailer. The retailer loses any unmet demand. We analyze three different scenarios of the Stackelberg game, namely no advance selling with disruption, advance selling without disruption, and advance selling with disruption. Our results indicate that advance selling can be used to mitigate the impact of supply disruption and at the same time could lead to an increase in the overall SC profit.     

Optimal procurement, disposal and pricing policies for managing rental goods

Consider a video rental retailer who procures DVDs or video cassettes from a distributor and rents them to the customers. To meet the time‐varying rental demand, the retailer needs to develop cost‐effective procurement and disposal policies. In this paper, we first present a base model in which the underlying rental demand is decreasing over time, backorders are not allowed and the disposal price is exogenous. For this base model, we show that the optimal procurement quantity is equal to the sum of effective demands (rental demand net of returns) over an integral number of periods, and the optimal disposal policy can be determined by solving a simple dynamic program with polynomial complexity. We then analyze the case of endogenous disposal prices and derive optimal disposal policies by solving a quadratic optimization problem with tree constraints. We also extend the base model to allow for backorders and to cases where the retailer has multiple procurement opportunities and a contractual period where disposals are not allowed. We show that the qualitative nature of the procurement policy is preserved in these cases and the optimal procurement and selling policies can be determined using similar dynamic programming algorithms.     

The benefits of a three-level coordinated distribution policy in the value chain

Several studies have addressed the “buyer–supplier” relationship both qualitatively and quantitatively. Accordingly, this study focuses specifically on shipment sizes, and the number of shipments made under a three-echelon model composed of a manufacturer, a distribution center, and a retailer. A joint model is proposed, in which the system relevant cost is significantly reduced. Each party’s total relevant cost loss was calculated and compared with its optimal strategy. While the retailer was the focal company, the other parties’ loss tended to be the largest.     

The value of information sharing in a supply chain with a seasonal demand process

This paper considers a two echelon seasonal supply chain model that consists of one supplier and one retailer, with the assumption that external demand from the customer follows a seasonal autoregressive moving average (SARMA) process, including marketing actions that cannot be deduced from the other parameters of the demand process. In our model, the supplier and the retailer employ order-up-to policy to replenish their inventory. In order to evaluate the value of information sharing in a two echelon seasonal supply chain, three levels of information sharing proposed by Yu, Yan, and Cheng (2002) are used. The results for optimal inventory policies under these three levels of information sharing are derived. We show that the seasonal effect has an important impact on optimal inventory policies of the supplier under the three levels of information sharing. Our findings also demonstrate that the replenishment of lead time must be less than the seasonal period in order to benefit from information sharing. Thus, this result provides managers with managerial insights to improve supply chain performance through information sharing integration partnerships.     

An integrated production and inventory model for a system comprising an assembly supply chain and a distribution network

This study investigates the production and inventory problem for a system comprising an assembly supply chain and a distribution network. A uniform lot size is produced uninterruptedly with a single setup at each production stage. Equal-sized batch shipment policy is applied to the whole system and the number of batches can be varied. All retailers have agreed on a joint replenishment policy with a common replenishment cycle. The objective is to determine the optimal common replenishment cycle, the number of batches of each production stage and retailer, all of which minimises the integrated total cost. Moreover, a new concept is introduced; namely, critical replenishment cycle. The replenishment cycle division (RCD) and recursive tightening (RT) methods are then developed to obtain the optimal solutions to the subject problem. Two theorems are verified to ensure the solutions obtained by the RCD and RT methods reaching the global optimum. An example is presented to illustrate the procedures involved in the RCD and RT methods.     

Coordination of split deliveries in one-warehouse multi-retailer distribution systems

In this paper, we consider a distribution system where a warehouse is responsible for replenishing the inventories at multiple retailers by a fleet of vehicles of limited capacity. If a distribution policy of the system involves split deliveries, that is, the inventory of at least one retailer is replenished by using multiple vehicle routes, the coordination of the deliveries can further reduce the inventory cost of the retailer. We consider the coordination where two split deliveries are realized by direct shipping and multiple-stop shipping, respectively. To the best of our knowledge, this kind of coordination was never studied in the literature but can find its application in inventory routing problems. This paper proposes and analyses a class of coordination policies for the split deliveries which can reduce the inventory costs of the retailers without increasing transportation costs. A non-linear programming model is established for formulating the class of polices. Because the optimal coordination policy corresponding to an optimal solution of the model may be hard to find and/or implement, two simple but effective coordination policies are proposed. The inventory cost savings realized by the two policies are evaluated analytically and algorithmically. Our theoretical analysis and computational experiments show that both policies are effective. Under certain conditions, they can save 50% of the inventory costs at the retailers without increasing transportation costs.     

Dynamic ordering and pricing for a perishable goods supply chain

The paper studies the combined problem of pricing and ordering for a perishable product supply chain with one supplier and one retailer in a finite horizon. The lifetime of the product is two periods and demand in each period is random and price-sensitive. In each period, the supplier determines first a wholesale price and then the retailer decides an order quantity and retail prices. We show that the optimal pricing strategy for the non-fresh product depends only on its inventory, and the optimal pricing strategy and the optimal order quantity for the fresh product depend only on the wholesale price and they have a constant relation. Moreover, the game between the retailer and the supplier for finite horizon is equivalent to a one period game with only one order. Thus, the optimal policies are identical at each period. For the additive and multiplicative demands, we further obtain equations to compute the optimal strategies. All of above results are extended into the infinite horizon case and longer lifetime products. Finally, a numerical analysis is given.     

The supplier's optimal guarantee policy in newsvendor finance

The retailer is a capital‐constrained newsvendor and can borrow money from the bank if necessary. To help the retailer get a bank loan at a lower interest rate, the supplier provides guarantee for the retailer's loan up to a prespecified amount. In a Stackelberg game, the supplier decides the wholesale price and the guarantee amount as a leader, and then the retailer determines the order quantity and the amount of the loan as a follower. The supplier is risk‐neutral while the retailer's risk preference is reflected by a spectral risk measure (risk‐neutral, risk‐averse, or risk‐seeking). For a given wholesale price and guarantee amount, the retailer's objective function is quasi‐concave in the order quantity. The optimal solutions for the supplier and the retailer are derived. The supplier's expected profit with optimized wholesale price increases with the guarantee amount, and thus the supplier's optimal policy is to provide a full guarantee for the retailer's loan. When the supplier can limit his guarantee responsibility by a proportion of the outstanding loan obligation, the supplier's optimal policy is also to provide a full guarantee. Even if the retailer incurs bankruptcy costs in the event of repayment default, the supplier's optimal guarantee policy remains the same in these two different forms of limited guarantee. However, when the wholesale price is exogenous, that is, not a decision variable, the full guarantee is not necessarily optimal for supplier.     

A supplier selection and order allocation problem with stochastic demands

We consider a system comprising a retailer and a set of candidate suppliers that operates within a finite planning horizon of multiple periods. The retailer replenishes its inventory from the suppliers and satisfies stochastic customer demands. At the beginning of each period, the retailer makes decisions on the replenishment quantity, supplier selection and order allocation among the selected suppliers. An optimisation problem is formulated to minimise the total expected system cost, which includes an outer level stochastic dynamic program for the optimal replenishment quantity and an inner level integer program for supplier selection and order allocation with a given replenishment quantity. For the inner level subproblem, we develop a polynomial algorithm to obtain optimal decisions. For the outer level subproblem, we propose an efficient heuristic for the system with integer-valued inventory, based on the structural properties of the system with real-valued inventory. We investigate the efficiency of the proposed solution approach, as well as the impact of parameters on the optimal replenishment decision with numerical experiments.     

Multi-item integrated supply chain model for deteriorating items with stock dependent demand under fuzzy random and bifuzzy environments

In this paper, we have investigated multi-item integrated production-inventory models of supplier and retailer with a constant rate of deterioration under stock dependent demand. Here we have considered supplier’s production cost as nonlinear function depending on production rate, retailers procurement cost exponentially depends on the credit period and suppliers transportation cost as a non-linear function of the amount of quantity purchased by the retailer. The models are optimized to get the value of the credit periods and total time of the supply chain cycle under the space and budget constraints. The models are also formulated under fuzzy random and bifuzzy environments. The ordering cost, procurement cost, selling price of retailer’s and holding costs, production cost, transportation cost, setup cost of the supplier’s and the total storage area and budget are taken in imprecise environments. To show the validity of the proposed models, few sensitivity analyses are also presented under the different rate of deterioration. The models are also discussed in non deteriorating items as a special case of the deteriorating items. The deterministic optimization models are formulated for minimizing the entire monetary value of the supply chain and solved using genetic algorithm (GA). A case study has been performed to illustrate those models numerically.     

Integrated inventory and transportation decision for ubiquitous supply chain management

We consider price-dependent demand and develop an integrated inventory and transportation policy with strategic pricing to maximize the total profit for a ubiquitous enterprise. The proposed policy provides the optimal ordering, shipment and pricing decision. We first assume that demand for a product is a linear function of the price. A mathematical model for the total profit under quantity based dispatch is developed in consideration of ordering, shipment and pricing variables. Optimality properties for the model are then obtained and an efficient algorithm is provided to compute the optimal parameters for ordering, shipment and pricing decision. Finally, we extend our results to a more general case where demand for the product is a convex or a concave function of the price.