Yong-Wu Zhou

Optimal production and shipment models for a single-vendor–single-buyer integrated system

Abstract This paper develops a more general production-inventory model for a single-vendor–single-buyer integrated system. Unlike the hitherto existing production-inventory models for the vendor–buyer system, the present model neither requires the buyer’s unit holding cost greater than the vendor’s nor assumes the structure of shipment policy. Secondly, the model is extended to the situation with shortages permitted, based on shortages being allowed to occur only for the buyer. Thirdly, the paper also presents a corresponding production-inventory model for a deteriorating item for the integrated system. The solution procedures are provided for finding the optimal production and shipment policies and illustrated with numerical examples. Three significant insights are shown: (1) no matter whether the buyer’s unit holding cost is greater than the vendor’s or not, the present model always performs best in reducing the average total cost as compared to the hitherto existing models; (2) if the buyer’s unit holding cost is less than the vendor’s, the optimal shipment policy for the integrated system will only comprise shipments with successive shipment sizes increasing by a fixed factor. It is different from that obtained by Hill [Hill, R.M., 1999. The optimal production and shipment policy for the single-vendor single-buyer integrated production-inventory problem. International Journal of Production Research 37, 2463–2475] for the opposite case; (3) when designing a single-vendor–single-buyer integrated system, making the buyer’s unit holding cost lower than the vendor’s is more beneficial to the system if shortages are not permitted to occur; otherwise it just reverses.

A stochastic and asymmetric-information framework for a dominant-manufacturer supply chain

Abstract Consider a dominant manufacturer wholesaling a product to a retailer, who in turn retails it to the consumers at

A multi-warehouse inventory model for items with time-varying demand and shortages

p/unit. The retail-market demand volume varies with p according to a given demand curve. This basic system is commonly modeled as a manufacturer-Stackelberg ([mS]) game under a “deterministic and symmetric-information” (“det-sym-i”) framework. We first explain the logical flaws of this framework, which are (i) the dominant manufacturer-leader will have a lower profit than the retailer under an iso-elastic demand curve; (ii) in some situations the system’s “correct solution” can be hyper-sensitive to minute changes in the demand curve; (iii) applying volume discounting while keeping the original [mS] profit-maximizing objective leads to an implausible degenerate solution in which the manufacturer has dictatorial power over the channel. We then present an extension of the “stochastic and asymmetric-information” (“sto-asy-i”) framework proposed in Lau and Lau [Lau, A., Lau, H.-S., 2005. Some two-echelon supply-chain games: Improving from deterministic–symmetric-information to stochastic-asymmetric-information models. European Journal of Operational Research 161 (1), 203–223], coupled with the notion that a profit-maximizing dominant manufacturer may implement not only [mS] but also “[pm]”—i.e., using a manufacturer-imposed maximum retail price. We show that this new framework resolves all the logical flaws stated above. Along the way, we also present a procedure for the dominant manufacturer to design a profit-maximizing volume-discount scheme using stochastic and asymmetric demand information. Using our sto-asy-i framework to resolve the logical flaws of the det-sym-i framework also reveals two noteworthy points: (i) the attractiveness of the perfectly legal but overlooked channel-coordination mechanism [pm]; and (ii) volume discounting as a means for the dominant manufacturer to benefit from information known only to the retailer.

Coordination of cooperative advertising models in a one-manufacturer two-retailer supply chain system

This paper develops a deterministic replenishment model with multiple warehouses (one is an owned warehouse and others are rented warehouses) possessing limited storage capacity. In this model, the replenishment rate is infinite. The demand rate is a function of time and increases at a decreasing rate. The stocks of rented warehouses are transported to owned warehouse in continuous release pattern. The model allows shortages in owned warehouse and permits part of the backlogged shortages to turn into lost sales--which is assumed to be a function of the currently backlogged amount. The solution procedure for finding the optimal replenishment policy is shown. As a special case of the model, the corresponding models with completely backlogged shortages and without shortages are also presented. The models are illustrated with the help of numerical examples. Sensitivity analysis of parameters is given in graphical form.

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

This paper considers cooperative advertising issues of a monopolistic manufacturer with competing duopolistic retailers. Four possible game structures (or power configurations), i.e., Stackelberg-Cournot, Stackelberg-Collusion, Nash-Cournot and Nash-Collusion, are discussed. Under each of four game structures, we develop a decision model for the three partners to design the optimal cooperative advertising policies. Through a comparison among the four models, we reveal how cooperative advertising policies and profits of all participants are affected by various competitive behaviors, and then determine whether the partners have any incentives to transit to a different structure. Also presented in the paper are a centralized decision model and a proposed cost-sharing contract, which is able to achieve perfect coordination of the considered channel, where the utility of risk preference is used to determine the fraction of local advertising costs shared by the manufacturer.

A comparison of different quantity discount pricing policies in a two-echelon channel with stochastic and asymmetric demand information

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 channels benefit rather than based on the buyers 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.

An EPQ model for deteriorating items with inventory-level-dependent demand and permissible delay in payments

Abstract In this paper, we study quantity discount pricing policies in a channel of one manufacturer and one retailer. The paper assumes that the channel faces a stochastic price-sensitive demand but the retailer can privately observe the realization of an uncertain demand parameter. The problem is analyzed as a Stackelberg game in which the manufacturer declares quantity discount pricing schemes to the retailer and then the retailer follows by selecting the retail price and associated quantity. Proposed in the paper are four quantity-discount pricing policies: “regular quantity discount”; “fixed percentage discount”; “incremental volume discount” and “fixed marginal-profit-rate discount”. Optimal solutions are derived, and numerical examples are presented to illustrate the efficiency of each discount policy.

An uncooperative order model for items with trade credit, inventory-dependent demand and limited displayed-shelf space

This article develops an inventory model for exponentially deteriorating items under conditions of permissible delay in payments. Unlike the existing related models, we assume that the items are replenished at a finite rate and the demand rate of the items is dependent on the current inventory level. The objective is to determine the optimal replenishment policies in order to maximise the systems average profit per unit of time. A simple method is shown for finding the optimal solution of the model based on the derived properties of the objective function. In addition, we deduce some previously published results as the special cases of the model. Finally, numerical examples are used to illustrate the proposed model. Some managerial insights are also inferred from the sensitive analysis of model parameters.

A perishable inventory model under stock-dependent selling rate and shortage-dependent partial backlogging with capacity constraint

This paper considers a two-echelon supply chain where a supplier sells a single product through a retailer, who faces an inventory-dependent demand. The supplier hopes to incentive the retailer to order more items by offering trade credit. The retailer places the ordered items on the display shelf (DS) with limited space and stocks the remaining items (if any) that exceed the shelf capacity in his/her backroom/warehouse (BW). From the supplier’s perspective, we focus mainly on under which conditions the supplier should offer trade credit and how he/she should design such trade credit policy and corresponding ordering policy to obtain much more benefits. From the retailer’s perspective, we discuss whether the retailer needs BW and exactly how many items need to be stocked in BW when the supplier offers trade credit. We formulate a “supplier-Stackelberg” game model, from which we obtain the conditions under which the presented simple trade credit policy not only increases the overall chain profit but also each member’s profit. We also show that the trade credit policy is always more beneficial to the retailer than to the supplier if it is offered.

Considering asymmetrical manufacturing cost information in a two-echelon system that uses price-only contracts

This article develops a deterministic inventory model for perishable items with stock-dependent selling rate. In the model, the unsatisfied demand is partial backlogged and the backlogged demand rate is dependent on the negative inventory level during the stock-out period. Furthermore, a ceiling is imposed on the number of on-display stocks because too much inventory leaves a negative impression on the buyer and the amount of shelf space is limited. Next, the existence and uniqueness of the solution to the problem under two cases are examined, respectively. Then a solution procedure is shown to find the optimal replenishment policy of the considered problem. At last, two numerical examples and a real case study are presented to illustrate the application of the developed model.