Teaching

—————————————————————————————————————
Kevin Shang
Joseph J. Ruvane, Jr. Professor
Professor of Operations Management
—————————————————————————————————————

Supply Chain Games: Beer Game and Cash Beer Game

I have developed two online simulation games to illustrate supply chain activities. The first one is the standard beer game (the Beer Game) commonly employed in the operations management (OM) course; the second is an augmented system by incorporating cash flows into the Beer Game. I refer to this new game as Cash Beer Game. This page mainly focuses on the Cash Beer Game. Below I provide the motivation, the logic behind the game, and a brief description of the game.

Motivation

The goal of supply chain management is to match supply with demand effectively by coordinating the activities of multiple firms involved in the production, distribution, and sales of a physical good. The performance of a supply chain depends on how well the material flows, information flows, and financial flows within the supply chain are coordinated. The intertwined relationships between these flows have made this coordination process challenging in practice. To demonstrate the challenge of coordination between the material and information flows to students, the Beer Game is often employed in OM courses. While a supply chain includes financial flows, they are seldom discussed in the OM curriculum. The recent financial crisis has demonstrated the importance of incorporating financial flows into operations decisions — many supply chains were disrupted because upstream firms failed to maintain their normal operations due to financial illiquidity. The Cash Beer Game is designed to illustrate the impact of cash flows on the inventory decisions.

The Logic Behind Cash Beer Game

Modigliani and Miller (1958) show that when the financial market is perfect, the operations decision and financial decision can be decoupled. The document “An Inventory System with Cash Flows” illustrates this point by considering a simple inventory model with cash flows. Specifically, we consider a firm that uses its available cash to purchase inventory. After paying the ordered inventory in each period, the firm can gain interest returns with rate r from the excess cash. On the other hand, if the firm does not have enough cash to pay for the ordered inventory, it has to borrow from an outside source with a borrowing rate d. In addition, the firm has to pay for the physical holding cost (e.g., warehousing, insurance, etc.) for excess inventory and backorder costs (e.g., overtime, expediting expenses) for inventory shortage. These are the actual tangible costs due to inventory. The objective is to maximize the expected working capital at the end of a finite-time horizon. Without considering the long-term assets and liabilities and the other entries in the balance sheet as in our model, this objective is the same as maximizing the net worth (equity) of the firm. When the financial market is perfect, i.e., d = r in our model, we show the model is reduced to the standard inventory model in which the holding (respectively, backorder) cost rate is equal to the physical holding (respectively, backorder) cost rate plus (respectively, minus) the financial holding cost rate. Thus, the inventory decision can be determined by the inventory level without considering the cash status. The resulting inventory system is employed in the Beer Game. On the other hand, when the financial market is not perfect, i.e., d > r (which is the case in reality), we show that maximizing the working capital is equivalent to minimizing the sum of the inventory-related costs (i.e., physical holding and backorder costs) and the cash-related costs (i.e., interest gain and borrowing costs). In this case, the cash state does influence the inventory decision. In particular, the optimal inventory policy depends on the total working capital. This motivates the formulation of the Cash Beer Game. The document “An Inventory System with Cash Flows” is based on Luo and Shang (2018) where a more general model with trade credit contracts is considered.

Pedagogical Objectives

The Beer Game

The pedagogical objective the Beer Game is two-fold. First, it helps students understand the interaction between order (information) and material flows due to inventory decisions. This facilitates the discussion for finite-horizon inventory models in the OM course. Second, the result of the game demonstrates a well-known supply-chain phenomenon, called the bullwhip effect, i.e., the variabilities of order and net inventory are amplified when moving along the supply to the upstream location (Lee et al. 1997). This helps students understand behavioral and operational causes that lead to the bullwhip effect.

The Cash Beer Game

The pedagogical objective of the Cash Beer Game is to let students understand the challenge of managing inventory and cash simultaneously, and how cash flow influences the inventory order decision. Students have to trade off not only the holding cost rate and the backorder cost rate, but also the interest gains and borrowing costs by choosing a right portfolio of assets (i.e., cash and inventory). To that end, we emphasize the importance of working capital management. We also introduce the optimal control policy, referred to as working-capital dependent base-stock policy. The key insight of the game is that when financial constraints exist, firms should be more conservative in making operational decisions. Financial integration strategies, such as fintech platform, cash pooling, subsidies, etc., can be discussed through this game.

Cash Beer Game Description

The Cash Beer Game is played similarly as the Beer Game. There are four players in a team, with each player on a team representing a role in a simplified serial supply chain: from upstream (the top of the supply chain) to downstream (the bottom), there is a Factory that brews beer, a Distributor that buys from the Factory and sells to a Wholesaler, a Wholesaler that buys from the Distributor and sells to a Retailer, and a Retailer that sells to customers. See the figure below. Note that information (orders for inventory) and cash flow up the supply chain, whereas material (beer) flows down the supply chain. Each player makes an inventory order decision in each period based on her or his the cash level, net inventory, and the order received from her or his downstream player.

The game is played over a series of rounds. In each round of the game, each player executes nine steps that, in essence, move materials (beer) down the supply chain, and move information (inventory orders) and cash up the supply chain. There is a two-period lead time on both the transmission of information upstream and the shipment of beer downstream. That is, when a retailer, wholesaler, distributor, or factory places an order, the upstream firm receives that order two rounds later, and when factory, distributor, or wholesaler ships beer downstream, the downstream firm receives the shipment two rounds later. The retailer has no shipment lead time, i.e., consumers instantly receive beer from the retailer when they demand it, if the retailer has stock available.

In each round of the game, each player has to execute the nine steps below.

  1. Observe the incoming order (from a downstream firm) or demand (from consumers).

  2. Attempt to fill the order (including outstanding backorders, if any) from inventory.

  3. Receive cash from a downstream firm for the ordered inventory in Step 1 (a retailer receives cash from consumer’s demand).

  4. Record remaining inventory or backorders, and calculate inventory holding cost (if net inventory is positive) or backorder cost (if net inventory is negative).

  5. Receive a shipment from upstream to inventory.

  6. Advance a shipment the upper stream supplier one position downstream.

  7. Transmit the previous round’s order to the supplier.

  8. Pay an upstream firm for the previous round’s inventory order to the supplier.

  9. Determine this round’s order quantity.

Step 3 and Step 8 are new steps compared to the Beer Game. These two steps together essentially move cash from downstream to upstream, which is the same direction as the information flow. In Step 3, the amount of cash received in the current period is equal to the incoming order quantity times the unit selling price; in Step 8. the amount of cash payment to the supplier is equal to the order quantity transmitted in Step 7 times unit purchase cost. In other words, the payment method used in this game is the so-called the pay-at-order scheme. Each player still makes an inventory order decision in Step 9 and this is the only decision that a player makes in each round. In each round, the inventory-related costs and cash-related costs are incurred. More specifically, the physical holding cost and physical backorder cost are calculated according to the net inventory level in Step 4. The cash related cost includes an interest gain (negative cost) if the cash level at the end of the round is positive and a borrowing cost if the cash level is negative. The cash level at the end of a round is equal to the initial cash level plus a downstream player’s payment received in Step 3 minus the physical inventory holding and backorder costs in Step 4 minus the inventory payment in Step 8.

A few caveats follow. First, from the sequence of events, it is clear that the timing of receiving order from a downstream player and transmitting order to an upstream player is the same as that of receiving cash from downstream and sending cash to upstream. This suggests that there is a two-period lead time in the cash transmission. Second, we do not assume that cash is a hard constraint that restricts the inventory order quantity. This allows a player to continue the game even if there is a deficit, but the cash deficit will incur a penalty cost, i.e., the borrowing rate times the negative cash level at the end of a round.  This assumes that some financial institutions are willing to lend short-term funds to firms with a borrowing rate.

During the game, the net inventory level and cash level are automatically calculated and each player only needs to make an inventory order decision in Step 9 by trading off the physical holding cost rate versus the physical backorder cost rate, and the borrowing rate versus the interest gain rate. For the latter tradeoff, this is due to the fact that the inventory order decision will affect the payment to the supplier, which, in turn, affects the cash level. A player attempts to clear the outstanding debt as soon as possible as the borrowing rate is larger than the interest return rate. We also assume that the return from selling the product is higher than that of cash return rate, so a player has a motivation to purchase the inventory.

Sample Snapshots of User Interface and Game Chart

   

The online Beer Game and the Cash Beer Game are developed by Professor Kevin Shang at Fuqua School of Business, Duke University. Copyright 2018-2020. All Rights Reserved.