Bacel Maddah

Periodic review (s, S) inventory model with permissible delay in payments

This paper investigates the effect of permissible delay in payments on ordering policies in a periodic review (s, S) inventory model with stochastic demand. A new mathematical model is developed, which is an extension to that of Veinott and Wagner (Mngt Sci 1965; 11: 525) who applied renewal theory and stationary probabilistic analysis to determine the equivalent average cost per review period. The performance of the model is validated using a custom-built simulation programme. In addition, two distribution-free heuristic methods of reasonable accuracy develop approximate optimal policies for practical purposes based only on the mean and the standard deviation of the demand. Numerical examples are presented with results discussed.

Allocation of Service Time in a Multiserver System

Reducing congestion is a primary concern in the design and analysis of queueing networks, especially in systems where sources of randomness are characterized by high variability. This paper considers a multiserver first-come, first-served (FCFS) queueing model where we arrange servers in two stations in series. All arrivals join the first service center, where they receive a maximum of T units of service. Arrivals with service requirements that exceed the threshold T join the second queue, where they receive their remaining service. For a variety of heavy tail service time distributions, characterized by large coefficient of variations, analytical and numerical comparisons show that our scheme provides better system performance than the standard parallel multiserver model in the sense of reducing the mean delay per customer in heavy traffic systems. Our model is likely to be useful in systems where high variability is a cause for degradation and where numerous service interruptions are not desired.

Optimizing assortment and pricing of multiple retail categories with cross-selling

This paper investigates the joint optimization of assortment and pricing decisions for complementary retail categories. Each category comprises substitutable items (e.g., different coffee brands) and the categories are related by cross-selling considerations that are empirically observed in marketing studies to be asymmetric in nature. That is, a subset of customers who purchase a product from a primary category (e.g., coffee) can opt to also buy from one or several complementary categories (e.g., sugar and/or coffee creamer). We propose a mixed-integer nonlinear program that maximizes the retailer’s profit by jointly optimizing assortment and pricing decisions for multiple categories under a classical deterministic maximum-surplus consumer choice model. A linear mixed-integer reformulation is developed which effectively enables an exact solution to relatively large problem instances using commercial optimization solvers. This is encouraging, because simpler product line optimization problems in the literature have posed significant computational challenges over the last decades and have been mostly tackled via heuristics. Moreover, our computational study indicates that overlooking cross-selling between retail categories can result in substantial profit losses, suboptimal (narrower) assortments, and inadequate prices.

Newsvendor pricing and assortment under Poisson decomposition

This article studies the structure of and the interdependence among the critical decisions on pricing, inventory, and assortment of a retailer’s product line. It considers substitutable retail products that are horizontally differentiated variants under a logit consumer choice model, within a newsvendor-type supply setting and homogeneous pricing. The focus of this article is on analyzing joint pricing and inventory decisions for a given assortment, within a natural Poisson decomposition setting, under a “multiplicative–additive” demand model, where both variance and coefficient of variation of the demand depend on the price. For this problem, a Taylor series-based approximation is developed for the inventory cost and its accuracy is subsequently demonstrated. It is then shown that, under this approximation, the expected profit is unimodal in the price, and sufficient conditions are provided for the “risky” price, at optimal inventory, to be above (or below) the “riskless” price, pertaining to a make-to-order system. It is also shown that inventory considerations alter the behavior of the risky price in demand and cost parameters. Furthermore, joint assortment and inventory decisions under exogenous pricing are considered, and the unimodularity of the expected profit in the assortment size is proven. Also, a comparative statics analysis is performed and insights are presented.

Reserve stock models: Deterioration and preventive replenishment

Reserve stocks are needed in a wide spectrum of industries from strategic oil reserves to tactical (machine buffer) reserves in manufacturing. One important aspect under-looked in research is the effect of deterioration, where a reserve stock, held for a long time, may be depleted gradually due to factors such as spoilage, evaporation, and leakage. We consider the common framework of a reserve stock that is utilized only when a supply interruption occurs. Supply outage occurs randomly and infrequently, and its duration is random. During the down time the reserve is depleted by demand, diverted from its main supply. We develop optimal stocking policies, for a reserve stock which deteriorates exponentially. These policies balance typical economic costs of ordering, holding, and shortage, as well as additional costs of deterioration and preventive measures. Our main results are showing that (i) deterioration significantly increases cost (up to 5%) and (ii) a preventive replenishment policy, with periodic restocking, can offset some of these additional costs. One side contribution is refining a classical reserve stock model (Hansmann, 1962).

Promoting impulse buying by allocating retail shelf space to grouped product categories

This paper addresses a problem where a retailer seeks to optimize store-wide shelf-space allocation in order to maximize the visibility of products to consumers and consequently stimulate impulse buying. We consider a setting where the retailer, because of product affinities or the retailer’s historical practice, has pre-clustered product categories into groups each of which must be assigned to a shelf. On the basis of its location in the store layout, each shelf is partitioned into contiguous shelf segments having different anticipated customer traffic densities. The retailer seeks to assign each group of product categories to a shelf, to determine the relative location of product categories within their assigned shelf, and to specify their allocated total shelf space within given lower/upper bounds. We propose a 0–1 integer programme that takes into account expected customer traffic densities within the store, groups of product categories, their relative profitability, and the desirability to keep certain product groups in the same aisle, with the objective of maximizing the impulse buying profit. The proposed model is grounded in a preprocessing scheme that explores feasible assignments of subsets of product groups to available aisles by iteratively solving an -hard subproblem and is numerically observed to greatly outperform an alternative mixed-integer programming formulation. We demonstrate the usefulness of and the enhanced tractability achieved by the proposed approach using a case study motivated by a grocery store in New England and a variety of simulated problem instances.

Pricing, Variety, and Inventory Decisions for Product Lines of Substitutable Items

Integrating operations and marketing decisions greatly benefits a firm. Marketing actions drive consumer demand, which significantly influences operations management (OM) decisions in areas such as capacity planning and inventory control. On the other hand, the marketing department of a firm relies on OM cost estimates in making decisions concerning pricing, variety, promotions, etc. In this chapter, we review recent research on pricing, assortment (or variety), and inventory decisions in retail operations management, which contribute to the growing literature on joint marketing/OM models (e.g., Eliashberg and Steinberg 1993; Griffin and Hauser 1992; Karmarkar 1996; Pekgun et al. 2006, 2008; Porteus and Whang 1991). Other important contributions of the reviewed works account for inventory costs in pricing and variety models and utilize realistic demand models based on consumer choice theory. These contributions are discussed below.

Continuous (s, S) policy with MMPP correlated demand

This work considers a continuous inventory replenishment system where demand is stochastic and dependent on the state of the environment. A Markov Modulated Poisson Process (MMPP) is utilized to model the demand process where the corresponding embedded Markov Chain represents the state of the environment. The equations to calculate the system inventory measures and the number of orders per unit time are obtained for a continuous, infinite horizon and dynamically changing (s, S) policy. An efficient optimization heuristic is presented and compared to the commonly used approach of approximating the demand-count process over the lead time with a Normal distribution. An investigation of the MMPP demand process is considered where we quantify the impact of variability in the demand-count process which is due to auto-correlation. Our findings indicate that when demand correlation is high, a dynamic control, where the (s, S) policy changes with state of the environment governing the MMPP, is highly superior to the commonly used “static” heuristics. We propose two dynamic policies of varying computational complexity, and cost efficiency, depending on the class of the product (one for class A, and one for classes B and C), to handle such high-correlation situations.

Optimal information exchange policies in integrated product development

This article considers information exchange in an Integrated Product Development (IPD) environment. First, a dynamic programming model is formulated that is able to capture upstream partial information flow in a two-activity IPD process. A simple threshold policy is derived that aids the downstream activity in deciding whether to consider or ignore this upstream information as a function of information quality and its associated setup and rework penalties. Then, this formulation is expanded to model analytically, for the first time, information flow in a three-activity IPD process. In this case, the focus is on aiding the midstream activity in deciding whether to consider or ignore partial upstream information, taking into consideration downstream concerns. Because it is difficult to derive threshold policies in this case, the dynamic program has to be solved directly and then an extensive Monte Carlo simulation study is performed to analyze the behavior of the optimal policy. The simulation results suggest several important insights regarding the timing and frequency of considering partial information in an IPD environment.

Optimal allocation of servers and processing time in a load balancing system

We consider the problem of allocating processing time in a multi-channel load balancing system by focusing on systems where processing times have distributions characterized by high variability. Our objective is to reduce congestion by routing jobs to servers based on their workload. Specifically, we arrange servers in two stations in series, and require that the load be balanced between the two stations. All arrivals join the first service center where they receive a maximum of T units of service. Arrivals with service requirements that exceed the value T join the second station where they receive their remaining service. For a variety of heavy tail service time distributions, characterized by high variability, analytical and numerical comparisons show that our scheme provides better system performance than the standard parallel multi-server model in the sense of reducing the mean delay per customer when the traffic intensity is not too low. In particular, we develop lower bounds on the traffic intensity and the service time coefficient of variation beyond which the balanced series system outperforms the parallel system.