An Inventory Model with Planned Shortages and Price Dependent Demand

Previous research has yielded a procedure for a retailer to determine the optimal lot size and selling price when a supplier offers all-unit quantity discounts and demand is a decreasing function of price. In this paper, we extend that research by allowing for shortages. An algorithm is presented that determines the optimal lot size, order level, and selling price for a class of demand functions, including the constant price-elasticity and linear demand functions.     

A Note on the Effect of Sudden Obsolescence on the Optimal Lot Size

In most management situations, the decision to hold inventory involves some element of obsolescence risk The traditional approach to this problem, in both theory and practice, is to incorporate obsolescence costs in the inventory holding cost. This note explores this issue and demonstrates that the traditional approach is appropriate for items subject to sudden obsolescence; that is, for items with demand lifetimes that are exponentially distributed.     

Freezing the Master Production Schedule: Implications for Fill Rate*

Previous research examining alternative ways of dealing with schedule instability has shown that freezing a portion of the master production schedule (MPS) is a cost effective way to reduce instability. While it is often argued that MPS freezing limits the firm's ability to react to changing customer needs, the impact of freezing on customer service is not well understood. We examined the impact of freezing a specified portion of the MPS on the average fill rate under a wide variety of conditions using controlled simulation experiments. The results show that freezing can be implemented without causing a severe reduction in customer service.     

A Comparison of Three Joint Ordering Inventory Policies*

This paper evaluates the performance of a joint ordering inventory policy which was first suggested and characterized by Renberg and Planche [14]. This paper shows that the policy is easily characterized for Poisson demands. This policy is then compared with two other joint ordering policies—the well-known (S, c, s) or can-order policy of Balintfy [3] and the recent periodic policies suggested by Atkins and lyogun [2]. For a continuous review operating environment, the Renberg and Planche policy utilizes a group reorder point and a combined order quantity (Q), with each item maintaining an order-up-to level (S). For the can-order policy, each item in the product group has a must-order point (s), a can-order point (c) and an order-up-to level (S). The periodic policies require that item orders be grouped at some fixed scheduled intervals. Using long-run total average costs as the basis, it is shown that no one policy is superior to the others in all the examples tested. In some cases, the Renberg and Planche policy performs surprisingly well.     

TOTAL SETUP LOT SIZING WITH QUANTITY DISCOUNTS*

Often, order quantity decisions are made by purchasers facing a price schedule of quantity discounts. Traditional solution procedures have consisted of the evaluation of total cost at numerous price-break points in search of the lowest total cost. This approach is tedious and not particularly informative, especially when one is faced with lengthy schedules. This paper presents a total setup lot-sizing model that reduces the computations required to find the least-total-cost quantity, given parameters from a supplier's price schedule. The parameters are first obtained by simple regression (graphical or computer) and in themselves can provide valuable insight for the purchaser's decision making. A total setup lot-sizing model is next developed to define a “critical interval” that contains the solution. The model and algorithm are tested under a variety of conditions. Their application offers the decision maker a convenient alternative to determine the best quantity to order from a tendered price schedule.     

Supporting Quick Response Through Scheduling of Make-to-Stock Production/Inventory Systems*

Scheduling of traditional job shops in make-to-order systems has seen extensive research over the past three decades. In such systems, performance is often related to various job completion metrics such as average flow time, average lateness, etc. This paper examines a scheduling problem in a make-to-stock environment where individual job completion measures are irrelevant. In this case, customer orders are satisfied through on-hand inventory where customer service is more closely related to the manufacturer's ability to quickly satisfy demand. We consider the role of scheduling in reducing inventories and improving customer service in the context of a manufacturer who assembles several different products on a single assembly line. We develop scheduling rules for such a system and experimentally compare their performance to those typically used in such environments. Our results indicate that rules which consider the inventory position and demand forecast outperform traditional fixed cycle rules.     

MODELING DEMAND DURING LEAD TIME*

This paper treats some of the important considerations in constructing an analytical model for the distribution of demand during lead time. It presents a formal model that can be developed along one of two lines. The first has order size and order intensity leading to a compound distribution of period demand, then period demand and lead time giving rise to a compound distribution of demand during lead time. The second has order intensity and lead time giving rise to a compound distribution of lead-time order intensity, then lead-time order intensity and order size leading to a compound distribution of demand during lead time. The paper also condenses the state of the art in a table and proposes some simple classification schemes that could help researchers extend that state of the art.     

Setup Reduction in the Economic Production Quantity Model

We present an analysis of setup cost reduction using the economic production quantity model. The objectives of the paper are to draw conclusions by investigating several classes of setup reduction functions and to provide a general solution procedure. We examine the trade-offs between reduced inventories and increased capital investment and show that given any hypothetical setup cost reduction function, we can determine whether the total relevant cost can be reduced and how the reduction is achieved.