Single Production Facility Research Articles

The economic lot scheduling problem: theory and practice

A common problem in many industries is the scheduling of many products through a single production facility where the setup times, production and demand rates of each product are different. Various heuristic solution methods have been devised for this “Economic Lot Scheduling Problem” such as the Common Cycle, Basic Period and Extended Basic Period approaches. In practical operations, such as the manufacture of polypropylene film for packaging considered in this paper, there are a number of considerations to take into account in determining the “optimal” schedule. The criteria of minimising the annual cost, the only criterion considered in the literature, is only one of these. For example, there is a tendency for the methods to produce excessively long cycle times, so that the assumption of stationarity of demand is no longer valid. This paper compares the alternative solution methods on a variety of problems from the literature and the case studied. It is found that a modified version of the Haessler EBP method is most appropriate for the general standard problem. In the particular situation studied, the setup times are product sequence dependent. This can be considered within the Common Cycle approach, but not the other two methods which require the use of a fixed setup cost per product. The resulting annual costs are much lower, indicating that the Common Cycle method, contrary to the general view in the literature, may be the best method for the sequence dependent setup times situation, provided the product sequence is first determined to minimise the total setup times. An efficient algorithm for solving this latter problem using Networks Flow Analysis is determined. Ways of extending the Extended Basic Period methods to include the product sequencing to minimise total setup times are suggested.

Random Review Production/Inventory Systems with Compound Poisson Demands and Arbitrary Processing Times

A production/inventory system is considered in which a single production facility produces items of a given type. The demand for the item is assumed to arrive according to a compound Poisson process. The time required to produce an item is assumed to follow an arbitrary distribution. An (s, S) policy is considered in which production stops at the instant that the inventory level is raised to S and production resumes at an inspection point when the inventory level is observed to have dropped to or below s for the first time. The time interval between two successive inspection points during a nonproduction period is a random variable which follows an arbitrary distribution. Under a cost structure which includes a set-up cost, a linear holding cost and a linear backorder cost, an expression for the expected cost per unit time is obtained for given control values. The operating cost during a cycle is shown to be convex in S for a given value of S-s. For the continuous review simple Poisson demand system, as well as some other special cases of the system considered here, it is shown that the expected cost per unit time is unimodal. Based on these properties, a procedure to find the optimal (s, S) policy is presented.

COMMON DUE-DATE ASSIGNMENT AND SCHEDULING FOR A SINGLE PROCESSOR TO MINIMIZE THE NUMBER OF TARDY JOBS

This paper considers the problem of assigning a common due-date to a set of simultaneously available jobs and sequencing them on a single production facility. The objective is to determine the optimal common due-date value and job sequence that jointly minimize a cost function based on the assigned due-date and the number of tardy jobs. It is shown that the optimal due-date coincides with one of the job completion times and ordering jobs in non-decreasing processing times yields an optimal sequence which in general is not unique. An efficient (polynomial-bound) algorithm to find the optimal solution is presented and an illustrative example is provided.

A Queueing Model to Analyze the Value of Centralized Inventory Information

Competitive pressures and technological improvements are leading many firms to consider centralized information systems to manage inventories and schedule production. We propose a simple model to explore the potential benefits of such coordination. The model represents two products competing for a single production facility. Simple Markovian behavior is assumed throughout. The key step in the analysis is the explicit solution of a queueing model with a novel priority discipline: Serve a customer from the class having the largest number of customers in the system.

Numerical evaluation of heuristics for the multi-item single-level capacitated lot-size problem

The problem considered is the determination of lot sizes for multiple products to be produced on a single production facility with limited capacity. An optimal solution to this lot-sizing problem within reasonable computer time is not available so far. However, various heuristic solution procedures have been proposed in the literature. In addition, so-called improvement steps can be used in order to improve the final solution obtained by the lot-sizing heuristic. In a simulation study, several well-known lot-sizing heuristics of the period-by-period type are compared and the effectiveness of improvement steps is investigated. Numerical results show that the lot-sizing heuristics considerably differ in their cost performance, especially when capacity constraints are tight and the average time between orders is high.

Planning lot sizes and capacity requirements in a single stage production system

The problem addressed in this paper is the determination of lot sizes for multiple products to be produced on a single production facility with limited capacity. Demand is assumed to be deterministic and time-varying and must be met without backordering. The objective is to minimize the sum of setup and inventory holding costs. A heuristic solution procedure of the period-by-period type is presented. Moreover, the interaction between lot sizing and smoothing of capacity requirements is investigated in a case study.

A noniterative multiproduct multiperiod production planning method

Production planning for multiple products on a single production facility over a time horizon requires minimizing the sum of production costs (regular time, overtime and subcontracting) and inventory carrying costs for meeting the known demands of the products. It is shown that the problem can be formulated and solved by a simple and noniterative method of ‘column minima’ even for multiple product situations.

The Simultaneous Determination of Plant and Leased Warehouse Capacities for a Firm Facing Uncertain Demand in Several Regions

Abstract For each of several regions a firm has forecasted a probability distribution of future annual demand, and the plan is to build a single production facility to serve this demand. Each region is served by a simple leased warehouse with a lease cost which is a linear function of capacity. Any regional demand exceeding warehouse capacity is lost. The cost of building the plant is a nonlinear function of its capacity, and the unit cost of producing the product and supplying it to a region is constant. We develop an efficient algorithm based on the Kuhn-Tucker conditions for simultaneously determining the plant and warehouse capacities which will maximize the firm's expected profit. The paper includes a numerical example demonstrating the use of this algorithm.

The Dynamic Lot-Sizing Problem for Multiple Items Under Limited Capacity

Abstract This paper addresses the problem of scheduling the timing and quantities of production of n different products over m periods for a single production facility with a prespecified capacity. We assume that the demand is deterministic and can vary from one period to another and from one product to another. The objective is to minimize the sum of production setup and inventory holding costs. For medium-size problems, optimal solution algorithms do not yet exist and therefore heuristic solution algorithms are of interest. Most of the existing heuristics make use of the “forward-pass” concept in one way or the other. Forward pass means we begin by determining the lot sizes for earlier periods before moving to study the later periods. In this paper we study the forward-pass approach as well as a different solution approach which we call the four-step algorithm. We develop the feasibility conditions for pure forward-pass algorithms. Finally, we perform a comparative evaluation study.

Production/inventory systems with a stochastic production rate under a continuous review policy

A single production facility is dedicated to producing one product with completed units going directly into inventory. The unit production time is a random variable. The demand for the product is given by a Poisson process and is supplied directly from inventory when available, or is backordered until it is produced by the production facility. Relevant costs are a linear inventory holding cost, a linear backorder cost, and a fixed setup cost for initiating a production run. The objective is to find a control policy that minimizes the expected cost per time unit. The problem may be modeled as an M/ G/1 queueing system, for which the optimal decision policy is a two-critical-number policy. Cost expressions are derived as functions of the policy parameters, and based on convexity properties of these cost expressions, an efficient search procedure is proposed for finding the optimal policy. Computational test results demonstrating the efficiency of the search procedure and the behavior of the optimal policy are presented.

Technical Note—A One-Product Production/Inventory Problem under Continuous Review Policy

A single production facility is dedicated to producing one type of product with completed units going directly into inventory. The demand for the product is governed by a Poisson process and is supplied directly to inventory when available, or is backordered until it is produced by the production facility. Relevant costs are a linear inventory holding cost, a linear backorder cost, a fixed setup cost for initiating a production run. The objective is to find a control policy to minimize the expected cost per time unit. It is shown that the problem may be modeled as an M/D/1 queueing system with the optimal policy being a two-critical-number policy. Cost expressions are derived as functions of the policy parameters, and based on a convexity property of these cost expressions, an efficient search procedure is proposed for finding the optimal policy. In computational tests that were performed on an IBM 360/65, optimal policies were computed in less than 1/8 second of CPU time.

The Multi-Product Production Cycling Problem

Abstract The multi-product production cycling problem is concerned with the determination of a production/inventory policy for a single capacitated production facility which is dedicated to producing a family of products. This paper studies this problem assuming stochastic demand. The one-product problem may be analyzed as a Markov decision problem and solved as such. For the multi-product problem, a heuristic decision rule is proposed based on the analysis of the one-product problem, and a new notion: the composite product. This heuristic is then tested by simulation on a series of problems, and is shown to be the most effective of the heuristics considered for the set of test problems

The Effectiveness of Three Heuristic Rules for Job Sequencing in a Single Production Facility

This paper examines the effectiveness of three heuristic rules used in production sequencing where the objective is to minimize the downtime due to setup changes. The effectiveness of these heuristic rules was evaluated under various conditions of job size and setup time distribution. The results of this analysis indicate that job conditions do affect the effectiveness of these three rules.

Three Heuristic Rules for Sequencing Jobs to a Single Production Facility

This paper presents the experimental performance of three elementary rules for sequencing jobs through a single production facility. The problem is a variant of the “traveling salesman problem.” It is presented in terms of the job sequencing problem because of practical constraints on problem solving methods encountered in this situation. The objective of the sequencing decision is to minimize the facility downtime or setup time over a finite batch of jobs. The study consists of examining the performance of the three heuristic rules in terms of two criteria. The first is the optimal downtime obtained by the branch and bound algorithm. The second is the downtime which results from a random sequencing of jobs through the facility. The sampling procedure considers different values of the variance of between-job setup times, the number of jobs in the sequencing batch, and the form of the distribution of setup times.