Amit Eynan

Effective and simple EOQ-like solutions for stochastic demand periodic review systems

Abstract In this paper we examine a periodic review system under stochastic demand with variable stockout costs. The optimal values for cycle length and amount of safety stock are difficult to obtain because one of the First Order Conditions does not have a closed form solution. However, by using a Taylor series expansion to approximate part of the cost function, we produce a simple cost function structure which is similar to that of deterministic models. We argue that this simple structure is also beneficial to promote the solution in other problems where coordination of cycles is required. To illustrate, we use the joint replenishment problem for multiple items under stochastic demand and suggest simple and efficient solution procedures.

Periodic review and joint replenishment in stochastic demand environments

In this paper we consider periodic review systems under stochastic demands. First, we study the single product periodic review problem and propose a simple solution procedure which is near optimal. Then, given the existence of this simple procedure, we study the joint replenishment problem for multiple items under stochastic demands and suggest simple heuristics which provide very good results. We find the simple procedures combined with the robustness of the cost function to be very attractive in other applications which require coordination of cycle times under stochastic demands.

Assemble to order and assemble in advance in a single‐period stochastic environment

Faced with stochastic demand, a firm may decide to assemble its products in advance or assemble them once actual demand is realized. In general, the production cost for items assembled in advance (AIA) is lower than for items assembled to order (ATO), because there is no need to expedite, and the production process can be planned and executed well in advance. On the other hand, items assembled in advance (AIA) for which there is no demand incur excessive and unnecessary assembly costs. The two policies, AIA and ATO, as well as a composite one, are compared and analyzed in light of these trade-offs. The composite model, which is shown as the dominating policy, is also extended to deal with the following two scenarios. The first assumes a loss of a fraction of the demand when demand cannot be satisfied from the shelf but rather through ATO. The second considers the effects of budget constraints on the total inventory cost.

Lot-splitting decisions and learning effects

We consider a lot-splitting model where the unit manufacturing time follows a learning curve. Our objective is to maximize the net present value of the total revenue collected at the delivery of the sublots. An algorithm is developed to solve the problem. Computational experiments are conducted to study the performance of two ‘convenient’ operational approaches, namely the equal sublot size approach and the equal time interval approach. The computational results suggest that these two solution approaches are nearly optimal and that the net present value of the total revenue becomes less sensitive to the sublot sizes as the learning effect increases.

The Benefits of Flexible Production Rates in the Economic Lot Scheduling Problem

This paper considers the economic lot scheduling problem in which a family of items is produced using a single machine. The flexible production approach allows alteration of production rates during a production run. This flexible approach is investigated within the common cycle framework using marginal analysis to obtain a simple optimal solution procedure. Consequently, managerial insight regarding the optimal solution as well as simple expressions for lower bounds on the savings vis-à-vis the rigid and traditional approaches are provided.

Benefiting from the risk-pooling effect: internal (component commonality) vs. external (demand reshape) efforts

Faced with uncertain demand for their products companies bear the associated burdens such as holding cost, spoilage and shrinkage for excess inventory and lost sales, expediting cost and shortage penalty upon stockouts. Consequently, much attention and effort are channelled toward the reduction of these costs. Component commonality promotes this endeavour by designing products to share some of their components. Consequently, the variability of demand for the components is reduced followed by a decrease in the management cost of materials. A recently introduced approach is demand reshape where firms attempt to influence some consumers to switch to a different product even though their original choice is available. Consequently, total variability of demand for the products is reduced as well as inventory management costs. As both approaches rely on the risk pooling effect to gain benefits, we explore the efficiencies of the two approaches; we compare performance and also investigate the potential benefits of employing both simultaneously.

The multi-location inventory centralization problem with first-come, first-served allocation

Abstract In this paper the multi-location inventory centralization problem is studied. Each location may be characterized by a unique selling price and unique consequences of stockouts, reflecting its market economic structure. The practice of such scenarios increases as more firms become involved in global (international) operations. The objective is to determine the initial inventory level which will maximize the expected profit when allocation of inventory is immediate to the time when demand is generated (i.e., first-come, first-served (FCFS)). It is shown that in spite of the fact that inventory allocation is contingent upon customers arrival processes generated in various locations, the problem can be expressed as a single location problem, where the interarrival process need not be considered. Furthermore, managers should not be averse to centralization fearing that customers from a less profitable location will “cannibalize” the potential greater profit from other locations.

Selling Finite Capacity in Bulks

We consider a firm that owns a limited capacity for the delivery of services or for the production of customized products. Potential buyers specify the amount of capacity they will require for the execution of their intended services, goods or projects. Based on the size of the requirement, the firm makes a bid while being challenged in various ways: (1) it only knows the underlying probability function from which its customers’ reservation prices are drawn, (2) arrival of additional future requests is stochastic, and, (3) the firm knows in advance neither the magnitude of these potential requests nor the buyers reservation price. The firm aims to maximize its expected profit by choosing its pricing mechanism. The fact that capacity is demanded in varying amounts distinguishes this problem from most available literature in which standard sizes are sold or partial fulfillment and displacement are permitted. Lacking such allowances presents a new challenge to the firm as in conjunction with pricing it should also address the issue of various sizes requests’ compatibility to achieve optimal utilization of its capacity in order to maximize expected profit. In this article, we consider two approaches of handling this problem: myopic and foresighted. We formulate and analyze the problem to obtain the firms optimal bidding decisions as well as managerial insight about the optimal bid level and its important role in coordinating buyers’ requests. Furthermore, due to this role, pricing patterns in this environment are different than those in standard unit sales.

How Vital Is Price to Compulsive Collectors

Collecting is a widespread consumer behavior, as an estimated third of all adults collects something. According to Belk, collecting is “the process of actively, selectively, and passionately acquiring and possessing things removed from ordinary use and perceived as part of a set of non-identical objects or experiences” (1995, p. 67). It is an intensely involving form of consumption that can become an addiction, obsession, and compulsion (Belk et al. 1991). Compulsive collecting can lead to a host of problems, including individual, family and societal. A scale measuring compulsive collecting has been recently developed and validated (Kukar-Kinney and Ridgway 2013). In this paper, we use that measure to examine the relationship between consumers’ reaction to price and compulsive collecting.