Multiple In‐Cycle Transshipments with Positive Delivery Times

We 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.     

Stabilized‐Cycle Strategy for Capacitated Lot Sizing with Multiple Products: Fill‐Rate Constraints in Rolling Schedules

In practice, deterministic, multi‐period lot‐sizing models are implemented in rolling schedules since this allows the revision of decisions beyond the frozen horizon. Thus, rolling schedules are able to take realizations and updated forecasts of uncertain data (e.g., customer demands) into account. Furthermore, it is common to hold safety stocks to ensure given service levels (e.g., fill rate). As we will show, this approach, implemented in rolling schedules, often results in increased setup and holding costs while (over‐)accomplishing given fill rates. A well‐known alternative to deterministic planning models are stochastic, static, multi‐period planning models used in the static uncertainty strategy, which results in stable plans. However, these models have a lack of flexibility to react to the realization of uncertain data. As a result, actual costs may differ widely from planned costs, and downside deviations of actual fill rates from those given are very high. We propose a new strategy, namely the stabilized cycle. This combines and expands upon ideas from the literature for minimizing setup and holding costs in rolling schedules, while controlling actual product‐specific fill rates for a finite reporting period. A computational study with a multi‐item capacitated medium‐term production planning model has been executed in rolling schedules. On the one hand, it demonstrates that the stabilized‐cycle strategy yields a good compromise between costs and downside deviations. Furthermore, the stabilized‐cycle strategy weakly dominates the order‐based strategy for both constant and seasonal demands.     

Contingency Strategies in Managing Supply Systems with Uncertain Lead‐Times

The globalization of markets and geographic dispersion of production facilities, combined with a heavy outsourcing of supply chain processes, have substantially increased the exposure of supply chains to supply lead‐times of long and uncertain nature. In this paper, we study the potential use of two contingency strategies on top of the conventionally used time buffer—statically planned safety lead‐time (SL)—approach to deal with the lead‐time uncertainty. These are (1) the ex‐ante planning for disruption safety stock (DSS) to be released when a “disruption” (in this case, late delivery of the order) occurs; and (2) the ex‐post dynamic emergency response (DER), which dynamically decides on the timing and size of an emergency order to be placed. Our work elaborates on the optimal parameter setting for these strategies, compares their added values when used to complement the traditional SL approach, and examines how the use of the contingency strategies affects the SL and corresponding cycle length of a periodic review system. Our research finds that: (1) the above contingency strategies reduce the reliance on the SL and are cost effective when the coefficient of variation (CV) of the uncertain lead‐time is high; (2) it is important to re‐optimize the SL to account for the contingency plans; and (3) re‐optimization of the cycle length to account for the presence of the contingency responses, as opposed to using an EOQ‐determined cycle length, does not significantly improve the cost performance. However, such re‐optimization does well in the SL approach when the CV of the uncertain lead‐time is high.     

Static and Dynamic Pricing of Excess Capacity in a Make‐to‐Order Environment

We consider a make‐to‐order manufacturer that serves two customer classes: core customers who pay a fixed negotiated price, and “fill‐in” customers who make submittal decisions based on the current price set by the firm. Using a Markovian queueing model, we determine how much the firm can gain by explicitly accounting for the status of its production facility in making pricing decisions. Specifically, we examine three pricing policies: (1) static, state‐independent pricing, (2) constant pricing up to a cutoff state, and (3) general state‐dependent pricing. We determine properties of each policy, and illustrate numerically the financial gains that the firm can achieve by following each policy as compared with simpler policies. Our main result is that constant pricing up to a cutoff state can dramatically outperform a state‐independent policy, while at the same time achieving most of the increase in revenue achievable from general state‐dependent pricing. Thus, we find that constant pricing up to a cutoff state presents an attractive tradeoff between ease of implementation and revenue gain. When the costs of policy design and implementation are taken into account, this simple heuristic may actually out‐perform general state‐dependent pricing in some settings.