For more than a year now, we've been hearing about how supply chain issues are causing shortages of everything from electronics and autos to meat and household products.

Then the news broke that hundreds of thousands of at-home COVID-19 test kits were about to expire just as they were being distributed, which illustrated a different type of supply chain issue: ineffective management of inventory. Jiang Zhang, PhD, professor of decision sciences and marketing in Adelphi’s Robert B. Willumstad School of Business, is doing highly innovative work aimed at developing strategies manufacturers can use to determine how to produce the right amount of inventory that results in neither a shortage of supply nor a warehouse full of excess product.

In his latest paper, “Single-Manufacturer Multi-Retailer Supply Chain Models with Discrete Stochastic Demand,” published in the 2021 issue of Sustainability, Dr. Zhang and his collaborators combine sophisticated mathematical modeling and game theory to provide the basis for a decision guide for producers who supply multiple retail outlets.

One example of a single manufacturer serving multiple retailers would be a manufacturer of kitchen appliances. It may sell to big box stores, large appliance chains, and small, local, mom-and-pop shops. Since demand is random—unlike snowblowers or air conditioners, which are largely seasonal—how does the company know how many refrigerators to make and how to structure the pricing for the various retail outlets? This is where decision science comes in.

Dr. Zhang and his collaborators are using a combination of game theory, economics and mathematical modeling to develop guides to support decision-making in these uncertain situations.

Among the approaches the researchers used was the application of game models. These included the Stackelberg leadership model, which is based on a leader-follower relationship among suppliers. In this model, the dominant provider in a market area openly makes a decision about pricing and supply, and the smaller providers follow suit, armed with that information.

In another model, known as the prisoner’s dilemma, no one shows their hand; each provider makes a decision without knowledge of the others’ plans. This fascinating model is based on the situation in which two prisoners, suspected of committing a crime together, are isolated and urged to confess. Each is concerned only with getting the shortest possible prison sentence for themselves and each must decide whether to confess without knowing their partner’s plan. Both prisoners, however, know the potential consequences of their decisions:

  • If both confess, they will likely be punished equally and less harshly.
  • If neither talks, both gamble on the possible outcomes of a trial.
  • If one confesses and turns against the other, the confessor could go free and the one who didn’t talk will get all the jail time.

How does this relate to supply chain planning? It illustrates that when parties are unwilling or unable to cooperate, the likely outcomes are unpredictable and potentially mutually destructive. Dr. Zhang and his colleagues quantify the factors of the Stackelberg and prisoner’s dilemma game models to lay the foundation for a decision-making model that can be applied by manufacturers to prevent select supply chain issues.

Clearly, the Stackelberg model is more transparent and likely to yield more predictable results in terms of supply chain management from the production and pricing end. But we live in a world where competition, rather than cooperation, often prevails.

Dr. Zhang highlights the computational complexity of supply chain management. “When you’re looking at supply chains, you have to consider what we call dimension barriers—that is, the number of suppliers, steps and distribution points required for the supply of the goods in question. As these factors vary greatly among product lines, so too do the challenges of creating a mathematical model that can be adapted and applied to diverse businesses.”

The team conducted an analysis of how the functions of a manufacturing operation might be represented in a mathematical model. This enabled them to develop an algorithm—a finite sequence of well-defined instructions—to develop a logic-based decision-making tool that manufacturers could use to improve the efficiency of production planning.

Dr. Zhang’s research project focused on both the “push” model of manufacturing (make to stock) and the “pull” model (make to order). Economy of scale brings cost down when larger quantities are produced, but neither the manufacturer nor the retailers want to be stuck with holding extra inventory. The decision to find the correct amount to produce, sell and buy is complex. Through this work, Dr. Zhang and his colleagues are doing their part to guide manufacturers toward making smart decisions—and improving one link of the now well-known supply chain.

This paper, “Single-Manufacturer Multi-Retailer Supply Chain Models with Discrete Stochastic Demand,” was co-authored by professors Yaqing Xu and Zihao Chen of the School of Economics and Management, Xidian University, and professor Yihua Wei of the School of Management, Shanghai University.

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