Cataloged from PDF version of article.A decentralized system of competing retailers that order and sell the same product in a sales season is studied. When a customer demand occurs at a stocked-out retailer, that retailer requests a unit to be transshipped from another retailer who charges a transshipment price. If this request is rejected, the unsatisfied customer may go to another retailer with a customer overflow probability. Each retailer decides on the initial order quantity from a manufacturer and on the acceptance/rejection of each transshipment request. For two retailers, we show that retailers' optimal transshipment policies are dynamic and characterized by chronologically nonincreasing inventory holdback levels. We analytically study the sensitivity of holdback levels to explain interesting findings, such as smaller retailers and geographically distant retailers benefit more from transshipments. Numerical experiments show that retailers substantially benefit from using optimal transshipment policies compared to no sharing. The expected sales increase in all but a handful of over 3,000 problem instances. Building on the two-retailer optimal policies, we suggest an effective heuristic transshipment policy for a multiretailer system
W e study a centralized inventory sharing system of two retailers that are replenished periodically. Between two replenishments, a unit can be transshipped to a stocked-out retailer from the other. It arrives a transshipment time later, during which the stocked-out retailer incurs backorder cost. Without transshipment, backorder cost is incurred until the next replenishment. Since the transshipment time is shorter than the time between two replenishments, transshipments can reduce the backorder cost at the stocked-out retailer and the holding costs at the other retailer. The system is directed by a centralized inventory manager, who minimizes the long-run average cost consisting of replenishment, holding, backorder, and transshipment costs. The transshipment policy is characterized by hold-back inventory levels, which are nonincreasing in the remaining time until the next replenishment. The transshipment policy differs from those in the literature because we allow for multiple transshipments between replenishments, positive transshipment times, and backorder costs. We also discuss the challenges associated with positive replenishment time and develop upper and lower bounds of average cost in this case. Bounds are numerically shown to have an average gap of 1.1%. A heuristic solution is based on the upper bound and differs from the optimal cost by at most this gap.
Purpose: The purpose of this paper is to study joint inventory and pricing strategy for a continuous inventory review system. While dynamic pricing decisions are often studied in the literature along with inventory management, the authors' aim in this study is to obtain a single long-run optimal price; also to gain insight about how to obtain the optimal price and inventory control variables simultaneously and then the benefits of joint optimization of the inventory and pricing decisions over the sequential optimization policy often followed in practice. Design/methodology/approach: A general (R;Q) policy system with fixed cost of ordering is modelled and then the case where unsatisfied demand is lost is studied. General forms of both the additive and multiplicative demand models are used to obtain structural results. Findings: By showing optimality conditions on the price and inventory decision variables, two algorithms on how to obtain optimal decision variables, one for additive and another for multiplicative demand-price model are provided. Through extensive numerical analyses, the potential profit increases are reported if the price and inventory problem are solved simultaneously instead of sequentially. In addition, the sensitivities of optimal decision variables to system parameters are revealed. Practical implications: Although there are several studies in the literature investigating emergency price change models, they use arbitrary exogenous prices menus. However, the value of a price change can be better appreciated if the long-run price is optimal for the system. Originality/value: Very few researchers have investigated constant price and inventory optimization, and while there are several past studies demonstrating the benefits of dynamic pricing over a static one, there still are not many findings on the benefit of joint price and inventory optimization. © Emerald Group Publishing Limited
This paper studies spare part transshipments between two service part facilities whose demands are correlated. Transshipments are used to reduce severity of part stock outs. Facilities are run by an inventory manager (IM) who minimizes replenishment, transshipment, and inventory costs. We show that the optimal transshipment policy is an inventory hold-back type; if the part inventory at a facility is less than or equal to its hold-back level, a transshipment request made for that part by a stocked out retailer is rejected. The hold-back levels increase toward the next replenishment of partsThis implies that transshipment requests are initially accepted until a critical time and afterwards they are rejected. A heuristic is designed using this critical time as the single decision variable. It performs within 0.7-1.8% of the optimal cost. Heuristic policies of no inventory sharing and complete sharing, respectively, perform within 3% and 2% of the optimal cost. Since the computation of hold-back levels and implementation of the optimal transshipments, respectively, require limited resources and little IM oversight, we advocate for the use of the optimal transshipment policy.
In a centrally managed system, inventory at a retailer can be transshipped to a stocked-out retailer to meet demand. As the inventory at the former retailer may be demanded by future customers of that retailer and transshipment time/cost is non-negligible, it can be more profitable to not transship in some situations. When unsatisfied demand is backordered, reassignment of inventory to a previously backordered demand can perhaps become profitable as demand uncertainty resolves over time. Despite this intuition, we prove that no reassignments are necessary for cost optimality under periodic holding cost accounting in a two-retailer system. This remains valid for multi-retailer systems according to numerical analyses. When holding costs are accounted for only at the end of each replenishment cycle, reassignments are necessary for optimality but insignificant in reducing the total cost. In most instances tested, the decrease in total cost from reassignments is below 2% for end of cycle holding cost accounting. These results simplify transshipment policies and facilitate finding good policies in both implementation and future studies, as reassignments can be omitted from consideration in optimization models under periodic holding cost accounting and in approximation models under cyclical cost accounting.
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