Reducing lost-sales rate in (T, R, L) inventory model with controllable lead time

In order to establish a good image and to enhance customer’s loyalty, many efforts such as upgrading the servicing facilities, maintaining a high quality of products and increasing expenditure on advertisement could be made by a selling shop. Naturally, an extra-added cost must be spent for these efforts and it is expected to have a result to reduce the shortage cost of lost-sales and the total expected annual cost. This paper explores a probabilistic inventory model with optimal lost-sales caused by investment due to two different types of cost functions. We consider that the lead time can be shortened at an extra crashing cost, which depends on the length of the lead time. Moreover, we assume that the lost-sales rate can also be reduced by capital investment. The purpose of this paper is to establish a (T, R, L) inventory model with controllable lead time and to analyze the effects of increasing two different types of investments to reduce the lost-sales rate, in which the review period, lead time and lost-sales rate are treated as decision variables. We first formulate the basic periodic review model mathematically with the capital investment to reduce lost-sales rate. Then two models are discussed, one with normally distributed protection interval demand and another with distribution-free case. For each model, two investment cost functional forms, logarithmic and power, are employed for lost-sales rate reduction. Two computational algorithms with the help of the software Matlab are furnished to determine the optimal solution. In addition, six numerical examples and sensitivity analysis are presented to illustrate the theoretical results and obtain some managerial insights. Finally, the effect of lost-sales rate reduction is investigated. By framing this new model, we observe that a significant amount of savings can be easily achieved to increase the competitive edge in business. The results in the numerical examples indicate that the savings of expected annual total cost are realized through lost-sales reduction.     

An improved algorithm for the minimax distribution-free inventory model with incident-oriented shortage costs

This article reconsiders Gallego's minimax distribution-free procedure. He created a two-point distribution to serve the most unfavorable case for estimating the expected cost of lost sales. We provide a reasonable condition to insure the existence and uniqueness of the optimal solution and the convergence of Gallego's method.     

A simple cost minimization procedure for the (Q, r) inventory system with a specified fixed cost per stockout occasion

For fast-moving A items, Silver et al. [E.A. Silver, D.F. Pyke, R. Peterson, Inventory Management and Production Planning and Scheduling, third ed., John Wiley & Sons, New York, NY, 1998] explore the (Q, r) inventory system with a specified cost per stockout occasion. However, a number of difficulties have impeded the implement of their solution procedure. That is, the total relevant cost function is not convex in general, so the convergence of the Silver et al.’s solution procedure to the optimal solution of the total relevant cost function is not necessarily true. An easier and more accurate solution procedure is proposed to overcome the shortcoming of the Silver et al.’s solution procedure.     

A (Q, R) inventory replenishment model with two delivery modes

Although splitting shipments across multiple delivery modes typically increases total shipping costs as a result of diseconomies of scale, it may offer certain benefits that can more than offset these costs. These benefits include a reduction in the probability of stockout and in the average inventory costs. We consider a single-stage inventory replenishment model that includes two delivery modes: a cheaper, less reliable mode, and another, more expensive but perfectly reliable mode. The high-reliability mode is only utilized in replenishment intervals in which the lead time of the less-reliable mode exceeds a certain value. This permits substituting the high-reliability mode for safety stock, to some degree. We characterize optimal replenishment decisions with these two modes, as well as the potential benefits of simultaneously using two delivery modes.     

On contracts for VMI program with continuous review (r, Q) policy

Based on continuous review (r, Q) policy, this paper deals with contracts for vendor managed inventory (VMI) program in a system comprising a single vendor and a single retailer. Two business scenarios that are popular in VMI program are “vendor with ownership” and “retailer with ownership”. Taking the system performance in centralized control as benchmark, we define a contract “perfect” if the contract can enable the system to be coordinated and can guarantee the program to be trusted. A revenue sharing contract is designed for vendor with ownership, and a franchising contract is designed for retailer with ownership. Without consideration of order policy and related costs at the vendor site, it is shown that one contract can perform satisfactorily and the other one is a perfect contract. With consideration of order policy and related costs at the vendor site, it is shown that one contract can perform satisfactorily and the performance of the other one depends on system parameters.     

On sufficient conditions for cost rate function unimodality in periodic review (s, S) inventory models

The cost rate function that arises in the stationary analysis of a class of periodic review regenerative inventory systems is known to be unimodal if the renewal density of the underlying demand sequence is decreasing. We prove that the same result holds, under zero leadtimes, if the renewal density is concave increasing.     

A modified (S − 1, S) inventory system for deteriorating items with Poisson demand and non-zero lead time

An inventory system is considered for continuous decaying items with non-zero lead time and stochastic demand when shortages are allowed and all unsatisfied demands are backlogged. In this research we consider orders as separate packages where replenishment is one-for-one and a modified base stock policy is applied. In this paper, a penalty cost is introduced for stochastic inventory models with decaying items when less than one unit of the product is delivered to the customers. The objective of the warehouse is to maximize his average profit. Since the concavity analysis of the model is extremely complicated, an upper bound is introduced and an algorithm is presented for finding the optimal solution. Finally, a numerical example is presented and sensitivity analysis is carried out for a number of important parameters.     

Reliability of a consecutive (r, s)-out-of-(m, n):F lattice system with conditions on the number of failed components in the system

A consecutive(r, s)-out-of-(m, n):F lattice system which is defined as a two-dimensional version of a consecutive k-out-of-n:F system is used as a reliability evaluation model for a sensor system, an X-ray diagnostic system, a pattern search system, etc. This system consists of m × n components arranged like an (m, n) matrix and fails iff the system has an (r, s) submatrix that contains all failed components. In this paper we deal a combined model of a k-out-of-mn:F and a consecutive (r, s)-out-of-(m, n):F lattice system. Namely, the system has one more condition of system down, that is the total number of failed components, in addition to that of a consecutive (r, s)-out-of-(m, n):F lattice system. We present a method to obtain reliability of the system. The proposed method obtains the reliability by using a combinatorial equation that does not depend on the system size. Some numerical examples are presented to show the relationship between component reliability and system reliability.