Compute the optimal order quantity and total cost

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Reference no: EM132243185

Assignment - Case Study

Dynamic Lot Sizing

The dynamic lot-size model in inventory theory, is a generalisation of the Economic Order Quantity (EOQ) model that takes into account that demand for the product varies over time.

Dynamic lot sizing sometimes refers to as 'Time-Varying Demand' as well. In contrast to EOQ model where demand is constant, in the time-varying deterministic demand model, demands of various periods are unlike. The variations can depend on different reasons. For example, production on a contract, which requires that certain quantities are delivered on specified dates. Note that we are still considering deterministic demand, i.e., all variations are known in advance. In the basic models, lead-time is disregarded. When dealing with lot sizing for time-varying demand, it is generally assumed that there are a finite number of discrete time steps, or periods. A period may be, for example, 1 day or a week. We know the demand in each period, and for simplicity, it is assumed that the period demand takes place at the beginning of the period. There is no initial stock. When delivering a batch, the whole batch is delivered at the same time. The holding cost and the ordering cost are constant over time. No backorders are allowed. We shall use the following notation:

Var	Definition
T =	number of periods,
d_i =	demand in period i, i = 1, 2, ..., T,
OC =	ordering cost,
HC =	holding cost per unit and time unit.

Problem -

Costco has received the following demands for a product in 2020:

Month	1	2	3	4	5	6	7	8	9	10	11	12
Demand	300	700	800	900	3300	200	600	900	200	300	1000	800

Suppose ordering cost (OC) is $504 and holding cost (HC) of one unit of product in a year is $3.

There is no shortage cost. Backordering is not allowed in this model.

To achieve the minimum total cost (ordering cost + holding cost), how many times the company should place orders in a year? In each order, how many products should be ordered? What is the total cost in a year?

Questions -

Q1. Given that the total demand of the whole year is 10,000 products, suppose the company is going to use the EOQ model for the accumulated demand of one year (10,000). In other words, ignore the monthly demand. Compute:

Optimal order quantity (Q*)
Total cost
Frequency of orders
Time between orders

Q2. Use mixed integer linear programming to solve the problem regarding the monthly demand. Suppose that holding cost is applied to the ending inventory.

Develop the mathematical model in the Word document.
Solve the problem in Excel.
Develop a plan in the Word document and explain when and how many products should be ordered in order to minimise the total cost.
Recalculate the optimal value of objective function (total cost with the new assumption that the holding cost is applied to the average inventory (not ending inventory).

Q3. Use 'Lot for Lot' heuristic method and compute the total cost.

Q4. Use 'Part Period Balancing' heuristic method, develop a schedule to show when and how many products should be ordered, and compute the total cost.

Q5. Use 'Silver_Meal' heuristic method, develop a schedule to show when and how many products should be ordered, and compute the total cost.

Note: Silver Meal heuristic method was coined by Gorham (1968).

Q6. Over the last five questions, you applied the methods which were explained in the videos. Now, it is your turn to research!

In this section, students are required to use Dynamic Programming based on the 'Wagner-Whitin' Algorithm to develop a schedule to show when and how many products should be ordered, and compute the total cost.

Summary - Put the results of all methods in a summary table and discuss.

Attachment:- Assignment File.rar

Reference no: EM132243185

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