DETERMINISTIC TIME‐VARYING DEMAND LOT‐SIZING MODELS WITH LEARNING AND FORGETTING IN SETUPS AND PRODUCTION

We study the deterministic time‐varying demand lot‐sizing problem in which learning and forgetting in setups and production are considered simultaneously. It is an extension of Chiu's work. We propose a near‐optimal forward dynamic programming algorithm and suggest the use of a good heuristic method in a situation in which the computational effort is extremely intolerable. Several important observations obtained from a two‐phase experiment verify the goodness of the proposed algorithm and the chosen heuristic method.     

A SINGLE-MACHINE SCHEDULING MODEL WITH FIXED-INTERVAL DELIVERIES

We consider an environment where a production facility modeled as a single machine needs to assign delivery dates to several orders and find a feasible sequence. Tardy jobs are not allowed. The delivery dates are to be at prespecified fixed intervals. The objective is to minimize the due date penalty and the cost of earliness. We provide a dynamic programming-based solution procedure that runs in polynomial time. We develop several dominance results that reduced the computational requirement by an order of magnitude in our computational study.     

CAPACITY AND PRODUCTION DECISIONS IN STOCHASTIC MANUFACTURING SYSTEMS: AN ASYMPTOTIC OPTIMAL HIERARCHICAL APPROACH

We present a new paradigm of hierarchical decision making in production planning and capacity expansion problems under uncertainty. We show that under reasonable assumptions, the strategic level management can base the capacity decision on aggregated information from the shopfloor, and the operational level management, given this decision, can derive a production plan for the system, without too large a loss in optimality when compared to simultaneous determination of optimal capacity and production decisions. The results are obtained via an asymptotic analysis of a manufacturing system with convex costs, constant demand, and with machines subject to random breakdown and repair. The decision variables are purchase time of a new machine at a given fixed cost and production plans before and after the purchase. The objective is to minimize the discounted costs of investment, production, inventories, and backlogs. If the rate of change in machine states such as up and down is assumed to be much larger than the rate of discounting costs, one obtains a simpler limiting problem in which the random capacity is replaced by its mean. We develop methods for constructing asymptotically optimal decisions for the original problem from the optimal decisions for the limiting problem. We obtain error estimates for these constructed decisions.     

A COMPARISON OF DIRECT COST SAVINGS BETWEEN FLEXIBLE AUTOMATION AND LABOR WITH LEARNING

This paper compares flexible automation with labor‐intensive manufacturing processes in a batch production environment and considers learning, forgetting, inventory carrying costs, setup costs, production demand volume, previous production experience, and the proportion of material to labor cost. While flexible automation typically can reduce setup times, and therefore inventory carrying costs through smaller optimal batch sizes, the results of this research show that the effect of forgetting on relative cost savings is difficult to predict in some situations. When using optimal lot sizes in both the automated and labor environments, cost savings from flexible automation may be smaller than expected or may occur in different ways than anticipated.     

OPTIMAL AND NEAR OPTIMAL CONTROL OF A TWO-PART-TYPE STOCHASTIC MANUFACTURING SYSTEM WITH DYNAMIC SETUPS

This paper deals with a manufacturing system consisting of a single machine subject to random failures and repairs. The machine can produce two types of parts. When the production is switched from one part type to the other, a random setup time is incurred at a constant cost rate. The objective is to track the demand, while keeping the work-in-process as close as possible to zero for both products. The problem is formulated as an optimal stochastic control problem. The optimal policy is obtained numerically by discretizing the continuous time continuous state opti-mality conditions using a Markov chain approximation technique. The discretized optimality conditions are shown to correspond to an infinite horizon, discrete time, discrete state dynamic programming problem. The optimal setup policy is shown to have two different structures depending on the parameters of the system. A heuristic policy is proposed to approximate the optimal setup policy. Simulation results show that the heuristic policy is a very good approximation for sufficiently reliable systems.     

A NOTE ON “COMMON DUE WINDOW SCHEDULING”

Kramer and Lee recently addressed a common due window scheduling problem with earliness and tardiness penalties, where earliness and tardiness penalty factors are constant and the common window size is given. They showed that the problem is polynomial when the location of the due window is a decision variable. For the case where the location of the due window is given, the problem is also polynomial when the latest due date is greater than or equal to the makespan, and they proposed a pseudopolynomial dynamic programming algorithm to find an optimal schedule when the latest due date is less than the makespan. In this note we address the problem for the case where the location of the due window is given. Specifically, we show that the problem is polynomial if the window location is unrestricted, and present a more efficient dynamic program algorithm to optimally solve the problem if the window location is restricted. The concepts of unrestricted and restricted window locations are defined in this note.     

COMMON DUE-WINDOW SCHEDULING

In this paper, we solve common due-window scheduling problems within the just-in-time window concept, i.e., scheduling problems including both earliness and tardiness penalties. We assume that jobs share the same due window and incur no penalty as long as they are completed within the due window. We further assume that the earliness and tardiness penalty factors are constant and that the size of the window is a given parameter. For cases where the location of the due window is a decision variable, we provide a polynomial algorithm with complexity O(n * log (n)) to solve the problem. For cases where the location of the due window is a given parameter, we use dynamic programming with pseudopolynomial complexity to solve the problem.     

PRODUCTION FLOW CONTROL FOR A MANUFACTURING SYSTEM WITH FLEXIBLE ROUTINGS

We study the dynamic routing problem for a flexible manufacturing system consisting of two unreliable machines and a finite buffer. One product-type is produced which requires two operations in sequence. The demand rate is assumed to be constant. Each machine is capable of performing both operations. The objective is to trace the demand while keeping the work-in-process low and the cycle-time short. An optimal control formulation is established for the dynamic routing problem. A production flow control algorithm is developed based on a combination of mathematical modeling and heuristics. The control policy is simulated and a comparison with the numerical optimal solution shows that it performs well for the instances under consideration.     

PRODUCTION SCHEDULING OF CONTINUOUS FLOW LINES: MULTIPLE PRODUCTS WITH SETUP TIMES AND COSTS

The problem of production planning and setup scheduling of multiple products on a single facility is studied in this paper. The facility can only produce one product at a time. A setup is required when the production switches from one type of product to another. Both setup times and setup costs are considered. The objective is to determine the setup schedule and production rate for each product that minimize the average total costs, which include the inventory, backlog, and setup costs. Under the assumption of a constant production rate, we obtain the optimal cyclic rotation schedule for the multiple products system. Besides the decision variables studied in the classical economic lot scheduling problem (ELSP), the production rate is also a decision variable in our model. We prove that our solutions improve the results of the classical ELSP.     

THEORIES AND REALITIES OF QUANTITY DISCOUNTS: AN EXPLORATORY STUDY

This paper compares and contrasts the current state of the art in the theory of quantity discounts with a field study of 39 firms. We start by categorizing and tabulating the literature pertaining to quantity discounts, and by summarizing the various studies and models according to their perspectives, assumptions, and characteristics. Next we describe current trends in industry with respect to the reasons why firms offer quantity discounts, the characteristics of discount schedules, and the effect of quantity discounts on the extent of centralized purchasing, number of suppliers, and just-in-time delivery. Finally, we identify a number of fruitful directions for future research.     

THE CLASSIC ECONOMIC PRODUCTION QUANTITY MODEL WITH SETUP COST AS A FUNCTION OF CAPITAL EXPENDITURE*

The formulation of the classic economic production quantity (EPQ) model is extended to include setup cost as a function of capital expense. Additional capital will buy reduced setup cost. Thus, the objective now is to balance holding, setup, and capital expenses. This new formulation is solved under conditions where setup cost varies exponentially and linearly as a function of capital expense. Decision rules are formulated to indicate under what conditions setup cost reduction reduces total cost. For the linear function, it is shown that once the decision to reduce setup cost is justified, the optimal choice is the minimum setup cost that is technologically feasible.     

TECHNICAL NOTE: A SIMPLE MODEL FOR OPTIMIZING THE SINGLE MACHINE EARLY/TARDY PROBLEM WITH SEQUENCE-DEPENDENT SETUPS

A simple mixed integer programming model for the N job/single machine scheduling problem with possibly sequence-dependent setup times, differing earliness/tardiness cost penalties, and variable due dates is proposed and evaluated for computational efficiency. Results indicated that the computational effort required to reach optimality rose with the number of jobs to be scheduled and with decreased variance in due dates. Though computational effort was significant for the largest problems solved, the model remained viable for optimizing research scale problems.     

AN ANALYSIS AND DISCUSSION OF THE OPTIMIZED PRODUCTION TECHNOLOGY SOFTWARE AND ITS USE

During the 19805 much attention, both pro and con, was directed toward optimized production technology (OPT). Criticism was directed at the proprietary nature of the scheduling algorithms within the software. Despite these criticisms, many large companies installed OPT. Little has been written on how the software is constructed and operates. This article introduces the software, provides a discussion of how it interfaces with management, and how various algorithms are imbedded in the software function. Last, a survey of companies that had implemented the software revealed that the major users are in the automotive industry.     

QUANTIFYING THE IMPACT OF INVENTORY HOLDING COST AND REACTIVE CAPACITY ON AN APPAREL MANUFACTURER'S PROFITABILITY

This paper was motivated by the operational problems faced by Northco, a school uniform manufacturer in the Northeastern United States. Northco was facing high working capital costs while also incurring high stockout and markdown costs. This paper models the impact of inventory holding cost and reactive capacity on Northco's targeted understocking and overstocking cost and offers a solution methodology for such problems. We quantify the impact of varying inventory carrying costs (and hence, high working capital costs) on stockout costs and the value of additional capacity. Our results illustrate that apparel manufacturers with high working capital costs, and hence high inventory carrying costs, should target higher stockout costs and achieve lower capacity utilization. The results presented have application beyond Northco because high working capital cost is endemic to many supply chains.     

OPTIMAL PROJECT SEQUENCING WITH RECOURSE AT A SCARCE RESOURCE

We develop a dynamic prioritization policy to optimally allocate a scarce resource among K projects, only one of which can be worked on at a time. When the projects' delay costs differ, the problem (a “restless bandit”) has not been solved in general. We consider the policy of working on the project with the highest expected delay loss as if the other project was completely finished first (although recourse is allowed). This policy is optimal if: (1) the delay cost increases with the delay regardless of the performance state, (2) costs are not discounted (or, discounting is dominated by delay costs), (3) projects are not abandoned based on their performance state during processing at the scarce resource, and (4) there are no stochastic delays. These assumptions are often fulfilled for processing at specialized resources, such as tests or one‐off analyses.     

AN EXPERIMENTAL MODEL FOR INVESTIGATING THE SENSITIVITY OF JOB SHOP PERFORMANCE TO JOB RELEASE TIME DISTRIBUTION PARAMETERS

Work flows in a job shop are influenced by the load per release and time interval between release factors. We focus on the latter factor, job release times. Building on Elvers' work, this study evaluates the impact of different job release time distributions on shop performance. Using a computer simulation of a random job shop and a full factorial experimental design, we demonstrate that the type of distribution does affect performance–a finding consistent with results from job shops characterized by good shop floor control practices. These findings are explained by examining the shape and variance traits of the underlying job release time distributions.     

MODELING LEARNING CURVE AND LEARNING COMPLEMENTARITY FOR RESOURCE ALLOCATION AND PRODUCTION SCHEDULING*

Research on learning effects in mathematical programming models for optimum resource allocation has called attention to the difficulty in solving such models in their original nonlinear form. In this paper, systematically varying sizes of linear segments are designed to approximate productivity changes along the learning curve, and a single separable linear programming model is developed. With production complementarity and learning transmission between products, a more realistic resource allocation and production scheduling problem emerges. Two cases of learning transmissions are considered, and the model design process, which defines a decision problem that can be solved by a simplex algorithm, is demonstrated.     

EXISTENCE AND DERIVATION OF FORECAST HORIZONS IN A DYNAMIC LOT SIZE MODEL WITH NONDECREASING HOLDING COSTS

We are concerned with a discrete-time undiscounted dynamic lot size model in which demand and the production setup cost are constant for an initial few periods and the holding cost of inventory is an arbitrary nondecreasing function assumed to be stationary (i.e., explicitly independent of time) in the same initial few periods. We show that there exists a finite forecast horizon in our model and obtain an explicit formula for it. In addition, we obtain fairly general conditions under which the existence of a solution horizon in the model implies the existence of a forecast horizon. We also derive an explicit formula for the minimal solution horizon. These results extend the earlier ones obtained for the dynamic lot size model with linearly increasing holding costs.     

COMBINED PRODUCTION AND MAINTENANCE SCHEDULING FOR A MULTIPLE‐PRODUCT,SINGLE‐ MACHINE PRODUCTION SYSTEM

Traditionally, the problems of equipment maintenance scheduling and production scheduling in a multi‐product environment have been treated independently. In this paper, we develop a Markov decision process model that simultaneously determines maintenance and production schedules for a multiple‐product, single‐machine production system, accounting for the fact that equipment condition can affect the yield of different product types differently. The problem was motivated by an application in semiconductor manufacturing. After examining structural properties of the optimal policy, we compare the combined method to an approach often used in practice. In the nearly 6,000 test problems studied, the reward from the combined method was an average of more than 25 percent greater than the reward from the traditional method.