Elizabeth M. Jewkes

Customer lead time management when both demand and price are lead time sensitive

In this paper, we model an operating system consisting of a firm and its customers, where the mean demand rate is a function of the guaranteed delivery time offered to the customers and of market price, where price itself is determined by the length of the delivery time. Economies of scale are present. The firms objective is to maximize profits by selecting an optimal guaranteed delivery time taking into account that (i) reducing delivery time will require investment, and (ii) the firm must be able to satisfy a pre-specified service level. We show that it is imperative for managers to know whether customers are price or lead time sensitive based on the simultaneous dependence of price and demand on delivery time before selecting a time-based competitive strategy. We investigate the optimal policy and provide managerial insights based on our analysis. Examples where our insights are consistent with actual practical situations are also provided. We show that our model is different from those in the literature that assume price and delivery time to be independent decision variables and present conditions under which ignoring the relation between price and delivery time can lead managers to substantially sub-optimal decisions - with or without the presence of economies of scale.

Calculating the benefits of vendor managed inventory in a manufacturer-retailer system

Firms such as Wal-Mart and Campbells Soup have successfully implemented vendor managed inventory (VMI). Articles in the trade press and academic literature often begin with the premise that VMI is ‘beneficial’; but beneficial to which party and under what conditions? We consider in this paper a vendor V that manufactures a particular product at a unique location. That item is sold to a single retailer, the customer C. Three cases are treated in detail: independent decision making (no agreement between the parties); VMI, whereby the supplier V initiates orders on behalf of C; and central decision making (both vendor and customer are controlled by the same corporate entity). Values of some cost parameters may vary between the three cases and each case may cause a different actor to be responsible for particular expenses. Under a constant demand rate, optimal solutions are obtained analytically for the customers order quantity, the vendors production quantity, hence the parties’ individual and total costs in the three cases. Inequalities are obtained to delineate those situations in which VMI is beneficial.

Integrated Production-Inventory-Distribution System Design with Risk Pooling: Model Formulation and Heuristic Solution

In this paper, we consider a multiproduct two-echelon production-inventory-distribution system design model that captures risk-pooling effects by consolidating the safety-stock inventory of the retailers at distribution centers (DCs). We propose a model that determines plant and DC locations, shipment levels from plants to the DCs, safety-stock levels at DCs, and the assignment of retailers to DCs by minimizing the sum of fixed facility location costs, transportation costs, and safety-stock costs. The model is formulated as a nonlinear mixed-integer programming problem and linearized using piecewise-linear functions. The formulation is strengthened using redundant constraints. Lagrangean relaxation is applied to decompose the problem by echelon. A lower bound is provided by the Lagrangean relaxation, while a heuristic is proposed that uses the solution of the subproblems to construct an overall feasible solution. Computational results reveal that the Lagrangean relaxation provides a sharp lower bound and a heuristic solution that is within 5% of the optimal solution.

Optimal and near-optimal inventory control policies for a make-to-order inventory-production system

Abstract This paper examines several inventory replenishment policies for a make-to-order inventory–production system that consists of a production workshop and a warehouse. Demands arrive to the production workshop according to a Poisson process, and are processed in an FCFS manner. The production workshop requires that the warehouse provides, as needed, raw materials for use in the production process. The warehouse inventory is replenished according to an inventory replenishment policy. The optimal replenishment policy, which minimizes the average total cost per product, is derived using a Markov decision process approach. The structure of the optimal replenishment policy is explored. Simple “order-up-to”, “myopic”, and heuristic replenishment policies are introduced. The myopic and heuristic replenishment policies are easy to compute, and yet perform almost as well as the optimal replenishment policy.

The value of information used in inventory control of a make-to-order inventory-production system

This paper studies a make-to-order inventory-production system consisting of a warehouse and a workshop. The concept of information level as the detail available on the number of unfilled demands at the workshop is introduced. The focal point is the value of the information used in inventory control in the warehouse. Dynamic programming is used to develop an algorithm for computing the optimal replenishment policy and the average total inventory cost per product. Numerical analysis is carried out and the results show that information used in inventory control can reduce the total inventory cost significantly. It is shown that the classical (Q, R) policy may not perform well if information about the number of demands is partially or fully available.

Response time reduction in make-to-order and assemble-to-order supply chain design

Make-to-order and assemble-to-order systems are successful business strategies in managing responsive supply chains, characterized by high product variety, highly variable customer demand and short product life cycles. These systems usually spell long customer response times due to congestion. Motivated by the strategic importance of response time reduction, this paper presents models for designing make-to-order and assemble-to-order supply chains under Poisson customer demand arrivals and general service time distributions. The make-to-order supply chain design model seeks to simultaneously determine the location and the capacity of distribution centers (DCs) and allocate stochastic customer demand to DCs by minimizing response time in addition to the fixed cost of opening DCs and equipping them with sufficient assembly capacity and the variable cost of serving customers. The problem is setup as a network of spatially distributed M/G/1 queues, modeled as a non-linear mixed-integer program, and linearized using a simple transformation and a piecewise linear approximation. An exact solution approach is presented that is based on the cutting plane method. Then, the problem of designing a two-echelon assemble-to-order supply chain comprising of plants and DCs serving a set of customers is considered. A Lagrangean heuristic is proposed that exploits the echelon structure of the problem and uses the solution methodology for the make-to-order problem. Computational results and managerial insights are provided. It is empirically shown that substantial reduction in response times can be achieved with minimal increase in total costs in the design of responsive supply chains. Furthermore, a supply chain configuration that considers congestion is proposed and its effect on the response time can be very different from the traditional configuration that ignores congestion.

Performance measures of a make-to-order inventory-production system

This paper develops two algorithms for computing the average total cost per product and other performance measures for a make-to-order inventory-production system. The two algorithms are developed by using matrix analytic methods. The first algorithm is based on the matrix-geometric solution of the Quasi-Birth-and-Death (QBD) Markov process. The second algorithm is based on the fundamental period of the QBD Markov process. The advantages and disadvantages of the two algorithms are discussed

A queueing model of delayed product differentiation

We consider a production system in which a supplier produces semi-finished items on a make-to-stock basis for a manufacturer that will customize the items on a make-to-order basis. The proportion of total processing time undertaken by the supplier determines how suitable the semi-finished items will be to meet customer demand. The manufacturer wishes to determine the optimal point of differentiation (the proportion of processing completed by the supplier) and its optimal semi-finished goods buffer size. We use matrix geometric methods to evaluate various performance measures for this system, and then, with enumeration techniques, obtain optimal solutions. We find that delayed product differentiation is attractive when the manufacturer can balance the costs of customer order fulfillment delay with the costs associated with unsuitable items.

Product differentiation and operations strategy in a capacitated environment

We study a firm selling two products/services, which are differentiated solely in their prices and delivery times, to two different customer segments in a capacitated environment. From a demand perspective, when both products are available to all customers, they act as substitutes, affecting each others demand. Customized products for each segment, on the other hand, result in independent demand for each product. From a supply perspective, the firm may either share the same capacity or may dedicate a different capacity for each segment. Our objective is to understand the interaction between product substitution and the firms operations strategy (dedicated versus shared capacity), and how this interaction shapes the optimal product differentiation strategy. We show that in a highly capacitated system, if the firm decides to move from a dedicated to a shared capacity setting, it will need to offer more differentiated products, whether the products are substitutable or not. In contrast, when independent products become substitutable, it results in a more homogeneous pricing scheme. Moreover, the optimal response to an increase in capacity cost also depends on the firms operations strategy. In a dedicated capacity scenario, the optimal response is always to offer more homogeneous prices and delivery times. In a shared capacity setting, it is always optimal to quote more homogeneous delivery times, but to increase or decrease the price differentiation depending on whether the status-quo capacity cost is high or low, respectively.

The Effectiveness of Investment in Lead Time Reduction for a Make-to-Stock Product

This paper focuses on a firm selling a make-to-stock product with a constant customer demand rate. The firm follows an exact (Q, r) policy for raw material inventory control and faces a random replenishment lead time. Through this research, we wish to gain a better understanding of the impact of investing in reducing supply lead time when the investment costs have to be borne, partly or fully, by the firm. This work is motivated by the recognition that lead time reduction is now of strategic importance in the successful operation of a firm. We examine different types of investment schemes in replenishment lead time reduction and the different cost models they generate. We present analytical and numerical results and insights for each type of model, compute the optimal (Q, r) policy and the associated investment levels. The work presents new results, and sheds light on some apparently counter-intuitive observations.