This question extends the RTT case in the class. Note that the data may be different from the ones in the slides and so make sure that you have the right numbers in your spreadsheet.

Red Tomato Tools $($RTT$)$ is a small manufacturer of gardening equipment. RTT$$s operations consist of the assembly of purchased parts into a multipurpose gardening tool. Due to minimal equipment and space requirements for their assembly operations, RTT$$s capacity is determined mainly by the size of its workforce.

The demand for RTT$$s gardening tools is highly seasonal, peaking in the spring as people plant their gardens. This seasonal demand ripples up the supply chain from the retailer to RTT$,$ the manufacturer. RTT has decided to use aggregate planning to overcome the obstacle of seasonal demand and maximize profits. The options RTT has for handling seasonality are adding workers during peak season, subcontracting out some of the work or building up inventory during the slow months. Customer satisfaction is key to RTT$,$ and all orders should be delivered to the customers on time. This means that no backlog orders are allowed. To determine how best to use these options through an aggregate plan, RTT$$s VP of supply chain starts the first task $$ building a demand forecast. This forecast is built in collaboration with its retailers. Table $1$ shows the cost and production data for RTT$.$

Currently, RTT has no limit on inventories. Inventory costs are incurred at the end of the month. RTT$$s goal is to obtain an ending inventory in June of at least $600$ units $($i$.$e$.$ no stock$-$outs at the end of June and a positive inventory$).$

Item

Material cost$/$unit

Inventory holding cost$/$unit$/$month Hiring and training cost$/$worker Layoff cost$/$worker

Labor hours required$/$unit

Regular time cost$/$hour

Overtime cost$/$hour

Marginal subcontracting cost$/$unit

Table $1$: Cost and production data for Red Tomato Tools.

Cost $$10$

$$2$ $$300$ $$500$

$4$ hours $$18$ $$27$ $$110$

RTT sells each tool to the retailer at $$115.$ The starting inventory in January is $1,000$ tools. At the beginning of January, the company has $50$ workers. The plant operates twenty days each month, and

$2$ Modified from: Chopra Sunil and Peter Meindl, Supply Chain Management: Strategy, Planning, and Operation Page $2$ of $4$

each employee earns $$18$ per hour in regular time. Each worker works $8$ hours a day of regular time with remaining hours performed on overtime. Machine capacity does not restrict production. Due to labor laws, no employee works more than $20$ hours of overtime per month.

Table $2$ shows the initial demand forecast developed for the six$-$month period beginning in January

Month January February March

April May June $3,6002,9002,300$

Demand forecast

$1,7002,9003,200$

Table $2$: Initial demand forecast for Red Tomato Tools.

a$)$ Determine how to optimize RTT$$s total costs.

b$)$ Do you think the subcontractor$$s pricing strategy is good? If yes, state your reasoning. If no$,$ at least

by how much should the subcontract reduce its price to become competitive?

c$)$ The warehouse manager found that there might be a potential problem with RTT$$s current

production schedule: the warehouse can only store up to $1,200$ units of finished goods. Does the current optimal solution satisfy this constraint? If not, modify the model as necessary, and re$-$run Solver to find the new optimal solution.

d$)$ Use your answer in c$)$ to answer this question. Suppose that the RTT$$s contract with its raw materials supplier ends in May and under its renewed contract, starting from June, raises to $$15/$unit$.$ Without re$-$running the solver, how would you expect the optimal solution and the optimal objective function to change $($and by how much$)?$ State your reasoning.