Part A (8 marks)
Demand and inventory on hand for five SKUs are presented in Table 2:

Given that the demands are deterministic and in manhours, and the available manhours (𝑃𝑡) for the period is 3000,
i. determine the sequence of producing the SKUs and show it in a simple graph.
ii. develop a linear programming model (in MS Word) and then solve it in Excel.
iii. explain the findings in details (MS Word)

iv. develop a table in which inventory position of all SKUs is presented for periods of switching the production for each SKU (MS Word and MS Excel). For inventory positions, round to the nearest integer and compute the sum of inventory on hand for each period.
v. Is maximization of T in conflict with the JIT paradigm where we try to achieve the minimum manufacturing cycle time?

Part B (8 marks)
Suppose we keep the information regarding the demand, inventory on hand, and the total production manhours from Part A. In this section, we want to avoid keeping excess inventory before the production begins. In other words, Renova starts to produce the items only when the inventory on hand is zero. You are required to
i. develop a linear programing model to provide an optimal production schedule for the five SKUs given that production starts when the inventory of an item is zero.
(MS Word)
ii. Solve the problem in Excel.
iii. Discuss your findings (MS Word).
iv. develop a table in which inventory position of all SKUs is presented for periods of switching the production for each SKU (MS Word and MS Excel). For inventory positions, round to the nearest integer and compute the sum of inventory on hand for each period.
v. Explain in which model (Part A or Part B), the probability of shortages is higher.
Why?. What is your recommendation?

Presentation (4 marks)
Organization, style, structure of sentences, flow of information, presenting the mathematical expressions in right format, citations and referencing, structure of tables and figures and the associated captions, and overall presentation.

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