Value of supplier's capacity information in a two-echelon supply chain

In traditional supply chain models it is generally assumed that full information is available to all parties involved. Although this seems reasonable, there are cases where chain members are independent agents and possess different levels of information. In this study, we analyze a two-echelon, single supplier-multiple retailers supply chain in a single-period setting where the capacity of the supplier is limited. Embedding the lack of information about the capacity of the supplier in the model, we aim to analyze the reaction of the retailers, compare it with the full-information case, and assess the value of information and the effects of information asymmetry using game theoretic analysis. In our numerical studies, we conclude that the value of information is highly dependent on the capacity conditions and estimates of the retailers, and having information is not necessarily beneficial to the retailers

Near-optimal modified base stock policies for the capacitated inventory problem with stochastic demand and fixed cost

In this study, we investigate a single-item, periodic-review inventory problem where the production capacity is limited and unmet demand is backordered. We assume that customer demand in each period is a stationary, discrete random variable. Linear holding and backorder cost are charged per unit at the end of a period. In addition to the variable cost charged per unit ordered, a positive fixed ordering cost is incurred with each order given. The optimization criterion is the minimization of the expected cost per period over a planning horizon. We investigate the infinite horizon problem by modeling the problem as a discrete-time Markov chain. We propose a heuristic for the problem based on a particular solution of this stationary model, and conduct a computational study on a set of instances, providing insight on the performance of the heuristic. © 2014 World Scientific Publishing Co

An iterative approximation scheme for repetitive Markov processes

Repetitive Markov processes form a class of processes where the generator matrix has a particular repeating form. Many queueing models fall in this category such as M/M/1 queues, quasi-birth-and-death processes, and processes with M/G/1 or GI/M/1 generator matrices. in this paper, a new iterative scheme is proposed for computing the stationary probabilities of such processes. An infinite state process is approximated by a finite state process by lumping an infinite number of states into a super-state. What we call the feedback rate, the conditional expected rate of flow from the super-state to the remaining states, given the process is in the super-state, is approximated simultaneously with the steady state probabilities. The method is theoretically developed and numerically tested for quasi-birth-and-death processes. It turns out that the new concept of the feedback rate can be effectively used in computing the stationary probabilities

A model for performance evaluation and stock optimization in a kit management problem

In this paper we consider a kit planning problem where demand occurrences are not for individual items, but for kits (a group of items). Each kit contains an arbitrary number of items. Kit demands occur according to a Poisson process. Whenever a kit demand occurs, only one item from the kit is used and the rest is returned as unused. The item that will be used from the kit is not known in advance and the whole kit has to stay at the demand site for the whole duration. The used item is replenished through a stochastic supply system, with possible capacity limitation. This model has applications in health care (planning surgical implant inventories), and repair kit management systems. As a demand for a kit triggers simultaneous demands for the items within the kit, the individual demand arrival processes for the items in that kit are correlated. Therefore, finding the joint probability distribution of the number of items that are outstanding, and hence finding the probability of kit availability, is generally difficult. We can obtain these terms in a fairly explicit form under the assumption that an item which is not in stock when a kit demand occurs can be obtained through borrowing from an emergency supply channel. As soon as a unit of such an item becomes available, it is returned back to its original supply source. We also formulate an optimization problem where the expected holding cost of items is minimized, and pre-specified kit availability constraints are satisfied. Since the optimization problem is hard to solve, we provide a heuristic procedure for obtaining the stock levels, and test the quality of the heuristic

Optimal inventory policies under imperfect advance demand information Optimal Inventory Policies under Imperfect Advance Demand Information

Abstract: We consider an inventory control problem where it is possible to collect some imperfect information on future demand. We refer to such information as imperfect Advance Demand Information (ADI), which may occur in different forms of applications. A simple example is a company that uses sales representatives to market its products, in which case the collection of sales representatives' information as to the number of customers interested in a product can generate an indication about the future sales of that product, hence it constitutes imperfect ADI. Other applications include internet retailing, Vendor Managed Inventory (VMI) applications and Collaborative Planning, Forecasting, and Replenishment (CPFR) environments. We develop a model that incorporates imperfect ADI with ordering decisions. Under our system settings, we show that the optimal policy is of order-up-to type, where the order level is a function of imperfect ADI. We also provide some characterizations of the optimal solution. We develop an expression for the expected cost benefits of imperfect ADI for the myopic problem. Our analytical and empirical findings reveal the conditions under which imperfect ADI is more valuable

Optimal inventory and pricing policies for remanufacturable leased products

In this paper we consider a company which leases new products and also sells remanufactured versions of the new product that become available at the end of their lease periods. When the amount of end-of-lease items in stock is not sufficient to meet the demand for remanufactured products, the firm may purchase additional cores from a third-party supplier. We develop a dynamic programming formulation for determining the optimal price of remanufactured products, and optimal payment structure for the leased products. Our objective is to maximize the discounted system-wide profit over a finite horizon. The profit function consists of revenues that are obtained from remanufactured product sales and leasing, remanufacturing and manufacturing costs, inventory holding and shortage costs. We consider a consumer choice based demand model for mapping a potential customer into one of the product segments (a remanufactured product customer or a customer for a leased product with a particular lease period) for a given price/lease payment vector. We explore several properties of the discounted profit function and provide insight on the behavior of pricing and inventory policies. We also investigate the effect of key product characteristics such as deterioration in age, cost of shortage in remanufacturable product inventory, and key market characteristics such as relative willingness-to-pay for buying a remanufactured product and relative willingness-to-pay for leasing a new product on optimal pricing policies through a computational study.Leasing Remanufacturing Pricing

Using imperfect advance demand information in ordering and rationing decisions

In this paper, we consider an inventory problem with two demand classes having different priorities. The appropriate policy of rationing the available stock, i.e. reserving some stock for meeting prospective future demand of preferred customers at the expense of deliberately losing some of the currently materialized demand of lower demand class(es), relies on the estimation of the future demand. Utilizing current signals on future demand, which we refer to as imperfect advance demand information (ADI), decreases uncertainty on future demand and may help to make better decisions on when to start rejecting lower class demand. We develop a model that incorporates imperfect ADI with inventory ordering (replenishment) decision and rationing available stock. In a two-period setting, we show some structural properties, solve the rationing problem, and propose solution methods based on Monte Carlo simulation for the ordering problem. We conduct numerical tests to measure the impact of system parameters on the expected value of imperfect ADI, and provide useful managerial insights.Inventory/production Advance demand information Customer reliability Periodic review Demand classes Rationing