Production Setup Cost Research Articles

Manufacturer-buyer coordination for newsvendor-type-products with two ordering opportunities and partial backorders

In a recent paper [Weng, Z.K., 2004. Coordinating order quantities between the manufacturer and the buyer: A generalized newsvendor model. European Journal of Operational Research 156, 148–161], a newsvendor-type coordination model was developed for a single-manufacturer single-buyer channel with two ordering opportunities. This paper further extends the model to the case where the excess demand after the first order is partially backlogged and both parties share the manufacturing setup cost of the second order (if happened). We show that the decentralized system would perform best if the manufacturer covers utterly the second production setup cost, which is opposite to that obtained in Weng (2004). Another extension in the present paper is that in the centralized system, the second order decision is made by the buyer based on the channel’s benefit rather than based on the buyer’s benefit as in Weng (2004). It is proved that the expected profit of the system in our paper is always larger than that in Weng (2004). In order to maximize the expected profit of the channel, two coordinated policies are proposed to achieve perfect coordination: a two-part-tariff policy for the special case that the buyer pays all the manufacturing setup cost, and a revised revenue-sharing contract for the case that two parties share the manufacturing setup cost.

Joint pricing and production planning for fixed priced multiple products with backorders

In this paper, we present a multiperiod model for production planning in a make-to-stock manufacturing system with constant pricing. We consider a multiproduct capacitated setting and introduce a demand-based model where the demand is a function of the price. There is an assumption that the production setup costs are negligible. A key part of the model is that backorders are allowed. As a result of this, the problem becomes a non linear programming problem with the nonlinearities in both the objective function and some constraints. We develop an algorithm that computes the global optimal production and pricing policy on a finite time horizon. We illustrate the application of the algorithm through a detailed numerical example.

Decomposition based heuristic algorithm for lot-sizing and scheduling problem treating time horizon as a continuum

In this paper, we deal with a new lot-sizing and scheduling problem (LSSP) that minimizes the sum of production cost, setup cost, and inventory cost. Incorporating the constraints of setup carry-over and overlapping as well as demand splitting, we develop a mixed integer programming (MIP) formulation. In the formulation, problem size does not increase as we enhance the precision level of a time period; for example, by dividing a time period into a number of microtime periods. Accordingly, in the proposed model, we treat the time horizon as a continuum not as a collection of discrete time periods. Since the problem is theoretically intractable, we develop a simple but efficient heuristic algorithm by devising a decomposition scheme coupled with a local search procedure. Even if in theory the heuristic may not guarantee finding a feasible solution, computational results demonstrate that the proposed algorithm is a viable choice in practice for finding good quality feasible solutions within acceptable time limit.

Single item lot-sizing with non-decreasing capacities

We consider the single item lot-sizing problem with capacities that are non-decreasing over time. When the cost function is (i) non-speculative or Wagner–Whitin (for instance, constant unit production costs and non-negative unit holding costs) and (ii) the production set-up costs are non-increasing over time, it is known that the minimum cost lot-sizing problem is polynomially solvable using dynamic programming. When the capacities are non-decreasing, we derive a compact mixed integer programming reformulation whose linear programming relaxation solves the lot-sizing problem to optimality when the objective function satisfies (i) and (ii). The formulation is based on mixing set relaxations and reduces to the (known) convex hull of solutions when the capacities are constant over time. We illustrate the use and potential effectiveness of this improved LP formulation on a few test instances, including instances with and without Wagner–Whitin costs, and with both non-decreasing and arbitrary capacities over time.

Single Item Lot-Sizing with Non-Decreasing Capacities

We consider the single item lot-sizing problem with capacities that are non-decreasing over time. When the cost function is i) non-speculative or Wagner-Whitin (for instance, constant unit production costs and non-negative unit holding costs), and ii) the production set-up costs are non-increasing over time, it is known that the minimum cost lotsizing problem is polynomially solvable using dynamic programming. When the capacities are non-decreasing, we derive a compact mixed integer programming reformulation whose linear programming relaxation solves the lot-sizing problem to optimality when the objective function satisfies i) and ii). The formulation is based on mixing set relaxations and reduces to the (known) convex hull of solutions when the capacities are constant over time. We illustrate the use and effectiveness of this improved LP formulation on a few test instances, including instances with and without Wagner-Whitin costs, and with both non-decreasing and arbitrary capacities over time.

An EPQ model with setup cost and process quality as functions of capital expenditure

This paper considers an economic production quantity (EPQ) model with imperfect production processes, in which the setup cost and process quality are functions of capital expenditure. The mathematical model is derived to investigate the effects of an imperfect production process on the optimal production cycle time when capital investment strategies in setup reduction and process quality improvement are adopted. An efficient procedure is developed to find the optimal production run length, setup cost and process quality. Finally, a numerical example is provided to illustrate the theoretical results. Some managerial implications are also included.

$${\cal K}$$ -Convexity1 in $$\Re^{n}$$

We generalize the concept of K-convexity to an n-dimensional Euclidean space. The resulting concept of \({\cal K}\)-convexity is useful in addressing production and inventory problems where there are individual product setup costs and/or joint setup costs. We derive some basic properties of \({\cal K}\)-convex functions. We conclude the paper with some suggestions for future research.

An algorithm for production planning in a flexible production system

In this paper, we consider the problem of determining the production rate, production batch size, and production sequence when production rate, setup cost, and unit processing cost are sequence-dependent. Using a standard lot sizing model with backorder, a tabu search algorithm for solving this problem is proposed. The algorithm is tested on some random test problems and its performance is compared with random sequencing. Computational results show that the proposed algorithm is very efficient.

Economic production cycles and setup reduction in an imperfect production system

This paper considers an economic production quantity model with imperfect production processes where the setup cost is function of capital expenditure. The mathematical model is derived to determine the optimal production run length and investment in setup cost reduction such that the total cost per unit time is minimized. In addition, an efficient algorithm is provided to find the optimal production run length and setup cost. A numerical example is provided to illustrate the results and to assess the cost savings realized by adopting investment strategy. Furthermore, some managerial implications are also included.

Multi-product inventory planning with downward substitution, stochastic demand and setup costs

In this paper we consider a single period multi-product inventory problem with stochastic demand, setup cost for production, and one-way product substitution in the downward direction. We model the problem as a two-stage integer stochastic program with recourse where the first stage variables determine which products to produce and how much to produce, and the second stage variables determine how the products are allocated to satisfy the realized demand. We exploit structural properties of the model and utilize a combination of optimization techniques including network flow, dynamic programming, and simulation-based optimization to develop effective heuristics. Through a computational study, we evaluate the performance of our heuristics by comparison with the corresponding optimal solution obtained from a large scale mixed integer linear program. The computational study indicates that our solution methodology can be very effective (98.8% on average) and can handle industrial-sized problems efficiently. We also provide several new qualitative insights on issues such as the effect of demand variance and cost parameters on the optimal number of products setup, the amount produced or inventoried, and the benefits of allowing substitution.

Optimization of the stochastic dynamic production cycling problem by a genetic algorithm

A production system to produce products of multiple items by several machines to meet time-varying stochastic demand is considered. The planning horizon is finite and divided into discrete periods. The demand in each period is mutually independent random variable whose probability distribution is known. Each machine can process at most one item in each period. Setup cost and setup time are incurred only when a machine changes from production of one item to another. Though this kind of problem can be formulated as a Markov decision model, it requires prohibitively long time to obtain a solution. Therefore, an eclectic model is proposed, where items are treated as variables to be determined at the beginning of the planning horizon and production quantities are determined as a policy. The objective function to be minimized is the expectation of the sum of production costs, inventory-holding costs, shortage costs and setup costs. A solution procedure consisting of a genetic algorithm and dynamic programming is proposed to obtain a near-optimal solution for the eclectic model. Three kinds of computational experiments are provided. First, we investigate preliminarily the difference between the optimal value for our eclectic model and the optimal value for the pure Markov decision model in which both items and production quantities are determined as a policy. It has been seen that the difference of the optimal values for the two models is small and the proposed eclectic model is effective. Secondly, we evaluate preliminarily the performance of the genetic algorithm itself for a deterministic model with a single machine that is a special case of the eclectic model. We have found that the genetic algorithm is so effective that we can apply it to the eclectic model. Thirdly, we provide main computational experiments to evaluate the performance of the proposed solution procedure consisting of the genetic algorithm and dynamic programming for the eclectic model. It has been found that good solutions can be obtained efficiently by the proposed solution procedure. Scope and purpose We deal with a production system to produce products of multiple items by several machines to meet time-varying stochastic demand. The planning horizon is finite and divided into discrete periods. Setup cost and setup time are incurred when a machine changes from production of one item to another. We should determine items and quantities of products produced on each machine in each period so as to minimize the expected sum of costs. This kind of problem is called a stochastic dynamic production cycling problem. Though it can be formulated as a Markov decision model, it requires a prohibitively long time to obtain a solution and is not practical. Therefore we propose an eclectic model that is easier to handle, where items are determined at the beginning of the planning horizon and production quantities are determined with the observed, actual inventory level. A branch and bound method is applicable for the eclectic model, but it is difficult to deal with larger problems. Instead we propose a solution procedure consisting of a genetic algorithm and dynamic programming to calculate a near-optimal solution for larger problems. The computational experiments show that the proposed eclectic model is effective and that good solutions for the eclectic model can be obtained efficiently by the proposed solution procedure.

Determination of economic production rate, production quantity and production sequence for flexible routing

In this paper, we consider the problem of determining the production rate, production batch size, and production sequence when production rate, setup cost, and unit processing cost are sequence-dependent. Using a standard lot sizing model with backorder, a tabu search algorithm for solving this problem is proposed. The algorithm is tested on random test problems and its performance is compared with random sequencing. Computational results show that the proposed algorithm is very efficient.

Models for a family of products with shelf life, and production and shortage costs in emerging markets

Many industrial products have very short life cycles as well as shelf-life constraints. Shelf-life does not necessarily reflect the physical condition of a product, it may reflect the productive or marketable life of a product as well in a competitive emerging market. In this paper, a production system that produces a family of items is considered and its policy is to produce all the items in every production cycle. A model is developed to incorporate the effects of constituent costs such as production cost, holding cost, setup cost, and shortage cost, which are four major costs in a typical inventory system with a shelf-life constraint. By using this model, a proper decision is reached to choose one of the three options: reduction of production rate, reduction of cycle time to avoid the violation of shelf-life constraint and adjusting to both of them simultaneously. An example is framed out to illustrate the mechanism of the models and a comparison between the proposed models with two previous models is also presented.

Simultaneous determination of the optimal production–inventory and product inspection policies for a deteriorating production system

In this paper, we attempt to find a method for the optimization of production–inventory and product inspection policies for deteriorating production systems. Taking advantage of the nature of a deteriorating production system, a strategy would be not to inspect the first s items of the batch. Therefore, an inspection policy which disregards the first s (DTF-s) items of the batch is proposed. Under the DTF-s policy, we do not inspect the first s produced items but inspect only those items from the (s+1)th till the end of the production run. The objective of this study was the joint determination of the production lot size and the inspection policy s, resulting in a minimization of the expected average cost per unit time. Based on this model, the underlying conditions necessary for the existence of an optimal policy are given. Two commonly used inspection strategies, no inspection and full inspection are discussed. Under both inspection strategies, an optimal production–inventory lot is bounded by the traditional economic quantity. The case of full inspection is shown to be an extension of previously reported results. The option of investing in the process of quality improvement is also discussed. Finally, numerical examples are given to illustrate the method and its advantages in the conclusion. Scope and purposeThis paper considers the relationship between production, inventory and inspection in a deteriorating production system which may transit from the “in-control” state to the “out-of-control” state after a period of operation. Once the transition to the “out-of-control” state has occurred, it is assumed that some percentage of the items produced are defective or of substandard quality. However, in many cases, defects in a defective item can only be identified by an inspection process which carries an inspection cost. Those inspected items which are found to be defective are reworked at some cost before being shipped. On the other hand, defective items which are not inspected will be passed to the customer, incurring a much larger warranty cost. In order to operate such a system economically, tradeoffs among production setup, inventory, inspection and defective cost must be analyzed. Deterioration of the production system is an inherent process in all manufacturing industries. An understanding of the relationship among production, inventory and inspection for such systems will help managers to maintain efficient and economic control of operations.

The effects of the warranty cost on the imperfect EMQ model with general discrete shift distribution

In this paper, we investigate the effect of the warranty cost on optimization of the economic manufacturing quality (EMQ). This is done for a deteriorating process where the production process shifts from the in-control state to the out-of-control state following a general discrete probability distribution. Once the production process goes out of control, the production process produces some defective items. The defective item cost includes reworking and warranty costs. Thus, in order to economically operate a production-inventory system with products sold under warranty, the tradeoffs among the production setup, inventory, and defective item cost, including the reworked cost before sale and the warranty cost after sale, needed to be analysed. This objective in this paper is to determine the production lot size while minimizing the total cost per unit of time per unit of time. Various special cases are presented. Two of them are extensions of results obtained previously in the literature. Finally, a numerical example is given which uses a discrete Weibull probability distribution. Sensitivity analysis of the model with respect to cost and time parameters is also performed.

Coordination of Pricing and Multiple-Period Production Across Multiple Constant Priced Goods

This paper addresses the problem of jointly determining prices and production schedules for a set of items that are produced on the same production equipment. Under the assumptions that the production setup costs are negligible and that demand is seasonal but price dependent, we exploit the special structure of the problem to develop a solution procedure. Through a set of numerical examples, we demonstrate how a product's contribution to aggregate seasonality can increase its optimal price. Our examples also demonstrate that, among products that experience demand peaks during the firm's busy season, those that peak early in the busy season should be priced more aggressively than those that peak later.

The eclectic model for stochastic dynamic production cycling problem

The production system to process multi-item products with a single machine by turns to meet time-varying stochastic demand in the finite planning horizon consisting of discrete periods is considered and a new optimization model and its calculation procedure are proposed. The problem is to determine the items and the production quantities to minimize the expectation of production costs, inventory-holding costs, shortage costs and setup costs. An eclectic model is built, where the items are treated as variables to be determined at the beginning of the planning horizon and the production quantities are determined as a policy. A calculation procedure using the branch and bound method is developed. Meaning and validity of the proposed model are clarified by a numerical example.

Integrated production-inventory models with imperfect production processes and a limited capacity for raw materials

This paper deals with inventory models that unify the decisions for raw materials and the finished product for a single product manufacturing system. The product is manufactured in batches and raw materials are jointly replenished from outside suppliers. The system is assumed to deteriorate during the production process. As a result, some proportion of nonconforming items is produced. The objective is to minimize the total variable cost for the system. A solution procedure is developed to find a near optimal solution for the basic model. The analysis for the basic model is extended to cases where the proportion of defective items is not constant or the defective rate is a function of production setup cost.

A generalized economic model for joint determination of production run, inspection schedule and control chart design

This paper presents a generalized model for a continuous production process for simultaneous determination of production quantity, inspection schedule and control chart design, with a non-zero inspection time for false alarms. Traditionally, the quality control problem and the inventory control problem have been viewed as two separate problems. Rahim (1994) developed an economic model for joint determination of production quantity, inspection schedule, and control chart design for a typical production process which is subject to a non-Markovian random shock. The model consists of the following cost components: (1) the production setup cost, (2) the inventory holding cost, and (3) the cost of maintaining the quality of the product under the surveillance of an x-chart. The optimal production quanity, the optimal inspection schedules, and the economic design parameters of the control charts were determined by striking a balance among these costs. For mathematical simplicity, it was assumed that production ceases only if the process was found to be out-of-control. However, in reality, this assumption may be inapplicable in many industrial situations. In many production processes the machine must be shut down when a search for the assignable cause is being carried out, even though occasionally the alarm turns out to be false. The purpose of this paper is to generalize the above model to cases where production ceases not only for a true alarm but also for a fixed amount of time whenever there is a false alarm. Examples of Weibull shock models are used to illustrate the proposed generalized model.

Formation of general GT cells: an operation-based approach

In this paper, we study the formation of general Group Technology cells based on the operation requirements of parts and operation capabilities of machines. Parts are first grouped into families by using a similarity coefficient based on common operation types. An integer model is then developed to solve the problem of machine group selection. The model takes into account machine cost, variable production cost, setup cost, and intracell material handling cost. A greedy heuristic, a minimum increment heuristic and a simulated annealing heuristic are proposed for solving the model more efficiently. The computational results have shown that the heuristic methods perform well when compared to the optimal solutions. The effect of changing cost structure on the performance of heuristic procedures is also investigated.