ALL: The goal is to minimize cost. Your payoffs are determined by the following equation that represents efficiency: Cases Moved×100×max{carry,backlog}Total Cost Total Cases Moved divided by Total Cost gives your per unit cost. The other component of the payoff functions as an adjustment term. If this objective function is ambiguous, remember to minimize your costs.
In this example we will follow a Wholesaler across two rounds to show the sequence of actions, costs, and timing issues. Each firm, including this wholesaler faces a carrying cost $C=$1 and a penalty cost $P=$2. At the start of the round the Wholesaler has 3 units in inventory and 0 backlog. There is an incoming delivery of 5 units and a 10 unit delivery is one week away.
Receive an incoming delivery | 5 units from Distributor |
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Update inventory | Now have 3 + 5 = 8 units in Inventory |
Receive incoming order | 6 unites from Retailer |
Send delivery | 6 units to Retailer |
Place your order | 7 units from Distributor |
At the end of the round there are two remaining units in inventory 8 - 6 = 2. Because $C=$1 there is a 2x$1= $2 carrying cost. Next round the 10 unit delivery will arrive. When will the 7 units ordered this round arrive (given a two week shipping delay)?
So even though you place your order in Round 4 you will not receive that order until Round 11! Let’s see what happens next round.
Receive an incoming delivery | 10 units from Distributor |
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Update inventory | Now have 2 + 10 = 12 units in Inventory |
Receive incoming order | 20 units from Retailer |
Send delivery | 12 units to Retailer |
Place your order | 20 units from Distributor |
At the end of the round there are no remaining units in inventory. The Retailer demanded 20 units and the Wholesaler was only able to send 12 units. Therefore, there are eight units in backlog. Because $P=$2, 8x$2= $16 penalty cost to their reputation for not being able to meet demand.
The Wholesaler placed an order for 20 units to the Distributor. However, the orders take one week to travel between each upstream firm (1 week to Distributor and then 1 week to Producer) and deliveries take two weeks to travel between each firm downstream (2 weeks from Producer to Distributor and then 2 weeks from Distributor to Wholesaler). That is a six week time horizon for orders.
Note that your time horizon for orders will differ depending on: